EXISTENCE AND UNIQUENESS FOR BOUNDARY-VALUE PROBLEM WITH ADDITIONAL SINGLE POINT CONDITIONS OF THE STOKES-BITSADZE SYSTEM
|
|
- Lawrence Pearson
- 5 years ago
- Views:
Transcription
1 Electronic Journal of Differential Equations, Vol (2012), No. 202, pp ISSN: URL: or ftp ejde.math.tstate.edu EXISTENCE AND UNIQUENESS FOR BOUNDARY-VALUE ROBLEM WITH ADDITIONAL SINGLE OINT CONDITIONS OF THE STOKES-BITSADZE SYSTEM MUHAMMAD TAHIR Abstract. This article shows the uniqueness of a solution to a Bitsadze system of equations, with a boundary-value problem that has four additional single point conditions. It also shows how to construct the solution. 1. Introduction The planar Stokes flow based on stream function ψ(, y) and stress function φ(, y), is epressed as φ φ yy = 4ηψ y, (1.1) φ y = η(ψ yy ψ ), where η is a material constant, see for the details [4, 5, 9]. The re-scaling (2ηψ ψ) reduces the system (1.1) to φ φ yy + 2ψ y = 0, ψ ψ yy 2φ y = 0, (1.2) which is the famous second order elliptic system called the Bitsadze system of equations and is identified as Stokes-Bitsadze system [10]. In the literature Bitsadze appears to have been the first to question the uniqueness and eistence or even the well-posedness of (1.2) subject to certain boundary conditions, see for reference [2, 3, 7]. Oshorov [8] finds well-posed problems for the Cauchy-Riemann system and etends those to the Bitsadze system (1.2). Vaitekhovich [12] discusses Dirichlet and Schwarz problems for the inhomogeneous Bitsadze equation for a circular ring domain. In the interior of unit disc a boundary value problem for the Bitsadze equation is considered by Babayan [1] and is proved to be Noetherian. In his paper Babayan also proposes solvability conditions for the inhomogeneous Bitsadze equation. The unique solvability in a unit disc for the inhomogeneous Bitsadze system is discussed in [6]. The Stokes-Bitsadze system (1.2) can be epressed in the matri form as AU + 2BU y + CU yy = 0, (1.3) 2000 Mathematics Subject Classification. 35J57. Key words and phrases. Bitsadze system; boundary value problem; single point conditions. c 2012 Teas State University - San Marcos. Submitted July 24, ublished November 15,
2 2 M. TAHIR EJDE-2012/202 where A = ( ) 1 0, B = 0 1 ( ) 0 1, C = A, U(, y) = 1 0 ( ) φ. ψ In a domain Ω R 2 with boundary Γ a linear boundary value problem of oincaré for the system (1.3) can be formulated as p 1 U + p 2 U y + qu = α(, y), (, y) Γ (1.4) where p 1, p 2, q are real 2 2 matrices and α(, y) a real vector given on the boundary Γ. The boundary-value problems of oincaré for the Stokes-Bitsadze system will be discussed elsewhere. In this paper we are interested in a boundary value problem with four additional single point conditions. 2. A boundary value problem with additional single point conditions We consider the Stokes-Bitsadze system (1.2) in domain Ω R 2 with boundary Γ subject to the following boundary conditions. and ψ = f, ψ n = g on Γ, (2.1) φ = φ, φ = ( φ), φ = ( φ), at a single point Ω. (2.2) Theorem 2.1. For f, g C(Γ), the boundary value problem (2.1) (2.2) for the Stokes-Bitsadze system (1.2) has a unique solution (φ, ψ) C 4 (Ω) C 4 (Ω). roof. Suppose φ, ψ C 4 (Ω). If (φ, ψ) satisfies (1.2), then φ and ψ are biharmonic in Ω, and for f, g C(Γ) the problem 2 ψ = 0 ψ = f ψ n = g in Ω on Γ on Γ (2.3) has a unique solution ψ C 4 (Ω), [11], that satisfies (1.2) and (2.1). Let the unique solution be denoted by ψ. Now we show that for the unique ψ if there eists φ satisfying (1.2) and (2.1) (2.2) then that φ is unique. Assume that the pairs (φ 1, ψ) and (φ 2, ψ) with φ 1 φ 2 satisfy (1.2) and (2.1) (2.2) and that δ = φ 1 φ 2. Then from (1.2) it immediately follows that But (2.2) then yields δ δ yy = 0, δ y = 0 on Ω. (2.4) δ = 0, δ = 0, δ = 0 at, (2.5) and the general solution of the system (2.4) becomes, δ = a + by + c( 2 + y 2 ) + d, (2.6) which on imposing the conditions (2.5) gives δ 0 in Ω and uniqueness of φ thus follows. Hence there eists at most one pair (φ, ψ) C 4 (Ω) C 4 (Ω) that can satisfy (1.2) and (2.1) (2.2). We are now in a position to assume (without proof) that ( φ, ψ) is a solution of (1.2) and (2.1) (2.2). Net, we suppose that (, ) and Q(, ) are the points in Ω, refer to the Figure 1.
3 EJDE-2012/202 EXISTENCE AND UNIQUENESS 3 Figure 1. Boundary conditions and additional single point conditions At point the epressions (1.2)(a) and (2.2)(c) respectively take the form φ φ yy = 2ψ y, φ + φ yy = φ, (2.7) from which it is obvious that φ and φ yy are known at. Since ( φ, ψ) satisfies (1.2)(b), therefore and on integration along Q we have φ yy (, ) = φ yy φ y (, ) = φ y φ yy = 1 2 [ ψ y ψ yyy ], (2.8) [ ψ y (λ, ) ψ yyy (λ, )]dλ, (2.9) [ ψ (λ, ) ψ yy (λ, )]dλ. (2.10) Since all the terms on right hand sides of (2.9) and (2.10) are known therefore φ yy and φ y are known along Q. Since ( φ, ψ) satisfies (1.2)(a), we have and using (2.9), can further be epressed as φ (, ) = φ yy φ = φ yy 2 ψ y, (2.11) [ ψ y (λ, ) ψ yyy (λ, )]dλ 2 ψ y (λ, ). (2.12) Further on integration along Q, we have [ φ (, ) = φ + φ yy + 1 µ ] [ 2 ψ y (λ, ) ψ yyy (λ, )] dλ dµ 2 ψy (λ, ) dλ, (2.13)
4 4 M. TAHIR EJDE-2012/202 whence φ(, ) = φ + ( )φ ( ) 2 φ yy 2 µ ν µ [ ψy (λ, ) ψ yyy (λ, ) ] dλ dµ dν. ψy (λ, )dλ dµ (2.14) Since all the terms on right hand sides of (2.11), (2.12), (2.13) are known therefore φ, φ and φ are known along Q and hence we know φ, φ and φ at Q(, ). Now from the point Q we draw the line QR where R(, y) Ω is an arbitrary point. Again, since ( φ, ψ) satisfies (1.2)(b); therefore which on integration, along QR, gives φ (, y) = φ (, ) φ (, y) = φ (, ) φ y = 1 2 [ ψ ψ yy ], (2.15) [ ψ (, λ) ψ yy (, λ)]dλ, (2.16) But the following epression from (1.2)(a) on integration along QR gives φ y (, y) = φ y (, ) + [ ψ (, λ) ψ yy (, λ)]dλ. (2.17) φ yy = φ + 2 ψ y, (2.18) Using (2.10) and (2.16) the epression (2.19) takes the form [ φ (, λ) + 2 ψ y (, λ)] dλ. (2.19) φ y (, y) = φ y µ [ ψ (λ, ) ψ yy (λ, )]dλ + (y ) φ (, ) [ ψ (, λ) ψ yy (, λ)]dλ dµ + 2 ψy (, λ)dλ. (2.20) Integrating along QR we obtain from (2.20) as follows. φ(, y) = φ(, ) + (y )φ y (y ) 2 φ (, ) (y ) [ ψ (λ, ) ψ yy (λ, )]dλ + 2 ν µ y y µ [ ψ (, λ) ψ yy (, λ)]dλ dµdν ψy (, λ)dλ dµ. (2.21)
5 EJDE-2012/202 EXISTENCE AND UNIQUENESS 5 Using (2.12) and (2.14) we finally obtain the following epression for φ(, y) at an arbitrary point (, y) Ω. φ(, y) = φ + ( )φ + (y )φ y [( ) 2 + (y ) 2 ]φ yy (y ) 2 ψy (, ) (y ) (y ) 2 2 µ ν µ [ ψ y (λ, ) ψ yyy (λ, )]dλ ψy (λ, ) dλ dµ + 2 y ν µ µ [ ψ (λ, ) ψ yy (λ, )] dλ ψy (, λ)dλ dµ [ ψ y (λ, ) ψ yyy (λ, )]dλ dµ dν [ ψ (, λ) ψ yy (, λ)]dλ dµ dν. (2.22) Obviously we have obtained an eplicit representation for φ in terms of the point conditions and ψ, on the assumption that ( φ, ψ) satisfies (1.2) and (2.1) (2.2). Net we show that ( φ, ψ) actually satisfies the Bitsadze system (1.2) and the conditions (2.2). From epression (2.22) it is easy to verify that φ(, ) = φ. We use (2.13) in (2.17) to obtain φ (, y) = φ + 2 [φ yy µ ψy (λ, ) dλ [ ψ y (λ, ) ψ yyy (λ, )]dλ] dµ [ ψ (, λ) ψ yy (, λ)]dλ, and it can be easily verified that φ (, ) = φ. Similarly from (2.10) and (2.20) we have φ y (, y) = φ y [ ψ (λ, ) ψ yy (λ, )] dλ + [ φ (, λ) + 2 ψ y (, λ)] dλ, and it follows that φ y (, ) = φ y. Again, from (2.12)and (2.16) we obtain φ (, y) = φ yy which at yields [ ψ y (λ, ) ψ yyy (λ, )] dλ 2 ψ y (, ) [ ψ (, λ) ψ yy (, λ)] dλ, φ (, ) = φ yy 2 ψ y (, ), (2.23) and from (2.7)(a) we obtain φ (, ) = φ. Also from (2.18) it is obvious that φ yy (, ) = φ (, ) + 2 ψ y (, ), (2.24) and (2.23) (2.24) yield φ yy (, ) = φ yy.
6 6 M. TAHIR EJDE-2012/202 Now we verify that φ(, y) satisfies (1.2)(a). differentiating with respect to we obtain Using (2.10) in (2.20) and then φ y (, y) = 1 2 [ ψ (, ) ψ yy (, )] (y )[ ψ y (, ) ψ yyy (, )] 2(y ) ψ y (, ) + 2 ψ (, y) 2 ψ (, ), µ which, since 2 ψ = 0, can be simplified as φ y (, y) y p [ ψ (, λ) ψ yy (, λ)] dλ dµ = 1 2 [3 ψ (, ) + ψ yy (, )] 1 2 (y )[3 ψ y (, ) + ψ yyy (, )] 1 2 [3 ψ (, ) + ψ yy (, y)] [3 ψ (, ) + ψ yy (, )] (2.25) (y )[3 ψ y (, ) + ψ yyy (, )] + 2 ψ (, y), and we obtain φ y (, y) = 1 2 [ ψ (, y) ψ yy (, y)]. (2.26) Then, to verify that φ(, y) satisfies (1.2)(b), we use (2.22) to obtain φ (, y) φ yy (, y) = (y ) 2 ψy (, ) (y )[ ψ (, ) ψ yy (, )] (y ) 2 [ ψ y (, ) ψ yyy (, )] µ y y ν µ y ψy (, λ)dλ dµ [ ψ y (λ, ) ψ yyy (λ, )] dλ [ ψ (, λ) ψ yy (, λ)] dλ dµ dν [ ψ y (λ, ) ψ yyy (λ, )]dλ 2 ψ y (, y) [ ψ (, λ) ψ yy (, λ)] dλ, which can further be simplified to obtain φ (, y) φ yy (, y) = 1 4 (y ) 2 [3 ψ y (, ) + ψ yyy (, )] 1 2 (y )[3 ψ (, ) + ψ yy (, )] 1 2 [3 ψ (, λ) + ψ yy (, λ)] dλ (y )[3 ψ (, ) + ψ yy (, )] (y ) 2 [3 ψ y (, ) + ψ yyy (, )]
7 EJDE-2012/202 EXISTENCE AND UNIQUENESS 7 2 ψ y (, y) and finally we have which completes the proof. [3 ψ (, λ) + ψ yy (, λ)]dλ, φ (, y) φ yy (, y) = 2 ψ y (, y), Conclusion. It has been proved by construction that there eists a unique solution ( φ, ψ) in C 4 (Ω) C 4 (Ω) to the Stokes-Bitsadze system (1.2) subject to the boundary conditions (2.1) along with additional single point conditions (2.2). Acknowledgements. The author is grateful to rofessor A. Russell Davies, Head School of Mathematics, Cardiff University, United Kingdom for his useful suggestions. References [1] A. H. Babayan; A boundary value problem for Bitsadze equation in the unit disc, J. Contemp. Math. Anal. 42(4) (2007) [2] A. V. Bitsadze; Some classes of partial differential equations, Gordon and Breach Science ublishers, New York, [3] A. V. Bitsadze; On the uniqueness of the solution of the Dirichlet problem for the elliptic partial differential operators, Uspekhi Mat. Nauk. 3(6) (1948) [4] C. J. Coleman; A contour integral formulation of plane creeping Newtonian flow, Q. J. Mech. appl. Math. XXXIV (1981) [5] A. R. Davies, J. Devlin; On corner flows of Oldroyd-B fluids, J. Non-Newtonian Fluid Mech. 50 (1993) [6] S. Hizliyel, M. Cagliyan; A boundary value problem for Bitsadze equation in matri form. Turkish J. Math. 35(1) (2011) [7] E. N. Kuzmin; On the Dirichlet problem for elliptic systems in space. Differential Equations, 3(1) (1967) [8] B. B. Oshorov; On boundary value problems for the Cauchy-Riemann and Bitsadze systems of equations, Doklady Mathematics 73(2) (2006) [9] R. G. Owens, T. N. hillips; Mass and momentum conserving spectral methods for Stokes flow, J. Comput. Appl. Math. 53 (1994) [10] M. Tahir; The Stokes-Bitsadze system, unjab Univ. J. Math. XXXII (1999) [11] A. N. Tikhonov, A. A. Samarskii; Equations of Mathematical hysics. ergamon ress Ltd. Oford, [12] T. Vaitekhovich; Boundary value problems to second order comple partial differential equations in a ring domain, Siauliai Math. Semin. 2 (10) (2007) Muhammad Tahir Mathematics Department, HITEC University, Taila Cantonment, akistan address: mtahir@hitecuni.edu.pk
RIEMANN-HILBERT PROBLEM FOR THE MOISIL-TEODORESCU SYSTEM IN MULTIPLE CONNECTED DOMAINS
Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 310, pp. 1 5. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu RIEMANN-HILBERT PROBLEM FOR THE MOISIL-TEODORESCU
More informationPROPERTIES OF SOLUTIONS TO NEUMANN-TRICOMI PROBLEMS FOR LAVRENT EV-BITSADZE EQUATIONS AT CORNER POINTS
Electronic Journal of Differential Equations, Vol. 24 24, No. 93, pp. 9. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu PROPERTIES OF SOLUTIONS TO
More informationINTRODUCTION TO PDEs
INTRODUCTION TO PDEs In this course we are interested in the numerical approximation of PDEs using finite difference methods (FDM). We will use some simple prototype boundary value problems (BVP) and initial
More informationINITIAL-BOUNDARY VALUE PROBLEMS FOR THE WAVE EQUATION. 1. Introduction In Ω = (0, 1) consider the one-dimensional potential u(x) =
Electronic Journal of Differential Equations, Vol. 4 (4), No. 48, pp. 6. ISSN: 7-669. URL: http://ejde.math.tstate.edu or http://ejde.math.unt.edu ftp ejde.math.tstate.edu INITIAL-BOUNDARY VALUE PROBLEMS
More informationZEROS OF THE JOST FUNCTION FOR A CLASS OF EXPONENTIALLY DECAYING POTENTIALS. 1. Introduction
Electronic Journal of Differential Equations, Vol. 20052005), No. 45, pp. 9. ISSN: 072-669. URL: http://ejde.math.tstate.edu or http://ejde.math.unt.edu ftp ejde.math.tstate.edu login: ftp) ZEROS OF THE
More informationSemigroups and Linear Partial Differential Equations with Delay
Journal of Mathematical Analysis and Applications 264, 1 2 (21 doi:1.16/jmaa.21.675, available online at http://www.idealibrary.com on Semigroups and Linear Partial Differential Equations with Delay András
More informationA non-local problem with integral conditions for hyperbolic equations
Electronic Journal of Differential Equations, Vol. 1999(1999), No. 45, pp. 1 6. ISSN: 17-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu ftp ejde.math.unt.edu (login:
More informationLIFE SPAN OF BLOW-UP SOLUTIONS FOR HIGHER-ORDER SEMILINEAR PARABOLIC EQUATIONS
Electronic Journal of Differential Equations, Vol. 21(21), No. 17, pp. 1 9. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu LIFE SPAN OF BLOW-UP
More informationMULTIPLE SOLUTIONS FOR THE p-laplace EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 2006(2006), No. 37, pp. 1 7. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) MULTIPLE
More informationSTOKES PROBLEM WITH SEVERAL TYPES OF BOUNDARY CONDITIONS IN AN EXTERIOR DOMAIN
Electronic Journal of Differential Equations, Vol. 2013 2013, No. 196, pp. 1 28. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu STOKES PROBLEM
More informationSEMILINEAR ELLIPTIC EQUATIONS WITH DEPENDENCE ON THE GRADIENT
Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 139, pp. 1 9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SEMILINEAR ELLIPTIC
More informationEXISTENCE OF POSITIVE SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS
Electronic Journal of Differential Equations, Vol. 013 013, No. 180, pp. 1 8. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF POSITIVE
More informationA LOWER BOUND FOR THE GRADIENT OF -HARMONIC FUNCTIONS Edi Rosset. 1. Introduction. u xi u xj u xi x j
Electronic Journal of Differential Equations, Vol. 1996(1996) No. 0, pp. 1 7. ISSN 107-6691. URL: http://ejde.math.swt.edu (147.6.103.110) telnet (login: ejde), ftp, and gopher access: ejde.math.swt.edu
More informationREGULARITY OF GENERALIZED NAVEIR-STOKES EQUATIONS IN TERMS OF DIRECTION OF THE VELOCITY
Electronic Journal of Differential Equations, Vol. 00(00), No. 05, pp. 5. ISSN: 07-669. UR: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu REGUARITY OF GENERAIZED NAVEIR-STOKES
More informationSOLVABILITY OF MULTIPOINT DIFFERENTIAL OPERATORS OF FIRST ORDER
Electronic Journal of Differential Equations, Vol. 2015 2015, No. 36, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SOLVABILITY OF MULTIPOINT
More informationSECOND-ORDER FULLY DISCRETIZED PROJECTION METHOD FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
Tenth MSU Conference on Differential Equations and Computational Simulations. Electronic Journal of Differential Equations, Conference 3 (06), pp. 9 0. ISSN: 07-669. URL: http://ejde.math.txstate.edu or
More informationSELF-ADJOINTNESS OF SCHRÖDINGER-TYPE OPERATORS WITH SINGULAR POTENTIALS ON MANIFOLDS OF BOUNDED GEOMETRY
Electronic Journal of Differential Equations, Vol. 2003(2003), No.??, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) SELF-ADJOINTNESS
More informationSPACE-TIME HOLOMORPHIC TIME-PERIODIC SOLUTIONS OF NAVIER-STOKES EQUATIONS. 1. Introduction We study Navier-Stokes equations in Lagrangean coordinates
Electronic Journal of Differential Equations, Vol. 2013 2013, No. 218, pp. 1 5. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SPACE-TIME HOLOMORPHIC
More informationBLOW-UP OF SOLUTIONS FOR A NONLINEAR WAVE EQUATION WITH NONNEGATIVE INITIAL ENERGY
Electronic Journal of Differential Equations, Vol. 213 (213, No. 115, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu BLOW-UP OF SOLUTIONS
More informationBoundary value problems for the elliptic sine Gordon equation in a semi strip
Boundary value problems for the elliptic sine Gordon equation in a semi strip Article Accepted Version Fokas, A. S., Lenells, J. and Pelloni, B. 3 Boundary value problems for the elliptic sine Gordon equation
More informationSYMMETRY IN REARRANGEMENT OPTIMIZATION PROBLEMS
Electronic Journal of Differential Equations, Vol. 2009(2009), No. 149, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SYMMETRY IN REARRANGEMENT
More informationEXISTENCE OF SOLUTIONS FOR CROSS CRITICAL EXPONENTIAL N-LAPLACIAN SYSTEMS
Electronic Journal of Differential Equations, Vol. 2014 (2014), o. 28, pp. 1 10. ISS: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTECE OF SOLUTIOS
More informationFUNCTIONAL COMPRESSION-EXPANSION FIXED POINT THEOREM
Electronic Journal of Differential Equations, Vol. 28(28), No. 22, pp. 1 12. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) FUNCTIONAL
More informationONE PROBLEM OF THE BENDING OF A PLATE FOR A CURVILINEAR QUADRANGULAR DOMAIN WITH A RECTILINEAR CUT. Kapanadze G., Gulua B.
Seminar of I. Veua Institute of Applied Mathematics REPORTS, Vol. 42, 2016 ONE PROBLEM OF THE BENDING OF A PLATE FOR A CURVILINEAR QUADRANGULAR DOMAIN WITH A RECTILINEAR CUT Kapanadze G., Gulua B. Abstract.
More informationA CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS
Math. J. Okayama Univ. 53 (2011, 167 172 A CAUCHY-KOWALEVSKI THEOREM FOR INFRAMONOGENIC FUNCTIONS Helmuth R. MALONEK, Dian PEÑA PEÑA and Frank SOMMEN Abstract. In this paper we prove a Cauchy-Kowalevski
More informationTHE EDDY CURRENT PROBLEM WITH TEMPERATURE DEPENDENT PERMEABILITY
Electronic Journal of Differential Equations, Vol. 003003, No. 91, pp. 1 5. ISSN: 107-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu login: ftp THE EDDY CURRENT PROBLEM
More informationNONLINEAR SCHRÖDINGER ELLIPTIC SYSTEMS INVOLVING EXPONENTIAL CRITICAL GROWTH IN R Introduction
Electronic Journal of Differential Equations, Vol. 014 (014), No. 59, pp. 1 1. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu NONLINEAR SCHRÖDINGER
More informationPOSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT BOUNDARY-VALUE PROBLEM. Ruyun Ma
Electronic Journal of Differential Equations, Vol. 1998(1998), No. 34, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) POSITIVE SOLUTIONS
More informationFunctions with orthogonal Hessian
Functions with orthogonal Hessian B. Dacorogna P. Marcellini E. Paolini Abstract A Dirichlet problem for orthogonal Hessians in two dimensions is eplicitly solved, by characterizing all piecewise C 2 functions
More informationPositive and monotone solutions of an m-point boundary-value problem
Electronic Journal of Differential Equations, Vol. 2002(2002), No.??, pp. 1 16. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) Positive and
More informationMULTIPLE POSITIVE SOLUTIONS FOR KIRCHHOFF PROBLEMS WITH SIGN-CHANGING POTENTIAL
Electronic Journal of Differential Equations, Vol. 015 015), No. 0, pp. 1 10. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu MULTIPLE POSITIVE SOLUTIONS
More informationBoundary Control of an Anti-Stable Wave Equation With Anti-Damping on the Uncontrolled Boundary
9 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 1-1, 9 WeC5. Boundary Control of an Anti-Stable Wave Equation With Anti-Damping on the Uncontrolled Boundary Andrey Smyshlyaev
More informationExplicit Jump Immersed Interface Method: Documentation for 2D Poisson Code
Eplicit Jump Immersed Interface Method: Documentation for 2D Poisson Code V. Rutka A. Wiegmann November 25, 2005 Abstract The Eplicit Jump Immersed Interface method is a powerful tool to solve elliptic
More informationEXISTENCE AND REGULARITY OF SOLUTIONS FOR STOKES SYSTEMS WITH NON-SMOOTH BOUNDARY DATA IN A POLYHEDRON
Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 147, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE AND REGULARITY OF SOLUTIONS FOR
More informationCOEFFICIENTS OF SINGULARITIES FOR A SIMPLY SUPPORTED PLATE PROBLEMS IN PLANE SECTORS
Electronic Journal of Differential Equations, Vol. 213 (213), No. 238, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu COEFFICIENTS OF SINGULARITIES
More informationMIXED BOUNDARY-VALUE PROBLEMS FOR QUANTUM HYDRODYNAMIC MODELS WITH SEMICONDUCTORS IN THERMAL EQUILIBRIUM
Electronic Journal of Differential Equations, Vol. 2005(2005), No. 123, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) MIXED
More informationExistence of solutions to a superlinear p-laplacian equation
Electronic Journal of Differential Equations, Vol. 2001(2001), No. 66,. 1 6. ISSN: 1072-6691. URL: htt://ejde.math.swt.edu or htt://ejde.math.unt.edu ft ejde.math.swt.edu (login: ft) Existence of solutions
More informationREPRESENTATION OF THE NORMING CONSTANTS BY TWO SPECTRA
Electronic Journal of Differential Equations, Vol. 0000, No. 59, pp. 0. ISSN: 07-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu REPRESENTATION OF THE NORMING
More informationGORDON TYPE THEOREM FOR MEASURE PERTURBATION
Electronic Journal of Differential Equations, Vol. 211 211, No. 111, pp. 1 9. ISSN: 172-6691. UL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu GODON TYPE THEOEM FO
More informationThe embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions
The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions Z. Jomaa and C. Macaskill School of Mathematics & Statistics University
More informationHYERS-ULAM STABILITY FOR SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 011 (011), No. 80, pp. 1 5. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu HYERS-ULAM STABILITY
More informationEXISTENCE OF POSITIVE SOLUTIONS OF A NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 215 (215), No. 236, pp. 1 7. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF POSITIVE
More informationA Robust Preconditioner for the Hessian System in Elliptic Optimal Control Problems
A Robust Preconditioner for the Hessian System in Elliptic Optimal Control Problems Etereldes Gonçalves 1, Tarek P. Mathew 1, Markus Sarkis 1,2, and Christian E. Schaerer 1 1 Instituto de Matemática Pura
More informationOSGOOD TYPE REGULARITY CRITERION FOR THE 3D NEWTON-BOUSSINESQ EQUATION
Electronic Journal of Differential Equations, Vol. 013 (013), No. 3, pp. 1 6. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu OSGOOD TYPE REGULARITY
More informationA Remark on -harmonic Functions on Riemannian Manifolds
Electronic Journal of ifferential Equations Vol. 1995(1995), No. 07, pp. 1-10. Published June 15, 1995. ISSN 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp (login: ftp) 147.26.103.110
More informationULAM-HYERS-RASSIAS STABILITY OF SEMILINEAR DIFFERENTIAL EQUATIONS WITH IMPULSES
Electronic Journal of Differential Equations, Vol. 213 (213), No. 172, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu ULAM-HYERS-RASSIAS
More informationSufficient conditions for functions to form Riesz bases in L 2 and applications to nonlinear boundary-value problems
Electronic Journal of Differential Equations, Vol. 200(200), No. 74, pp. 0. ISSN: 072-669. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) Sufficient conditions
More informationA PROPERTY OF SOBOLEV SPACES ON COMPLETE RIEMANNIAN MANIFOLDS
Electronic Journal of Differential Equations, Vol. 2005(2005), No.??, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) A PROPERTY
More informationVANISHING VISCOSITY LIMIT FOR THE 3D NONHOMOGENEOUS INCOMPRESSIBLE NAVIER-STOKES EQUATION WITH SPECIAL SLIP BOUNDARY CONDITION
Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 169, pp. 1 13. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu VANISHING VISCOSITY LIMIT FOR THE 3D NONHOMOGENEOUS
More informationADI iterations for. general elliptic problems. John Strain Mathematics Department UC Berkeley July 2013
ADI iterations for general elliptic problems John Strain Mathematics Department UC Berkeley July 2013 1 OVERVIEW Classical alternating direction implicit (ADI) iteration Essentially optimal in simple domains
More informationELLIPTIC EQUATIONS WITH MEASURE DATA IN ORLICZ SPACES
Electronic Journal of Differential Equations, Vol. 2008(2008), No. 76, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) ELLIPTIC
More informationEXISTENCE OF SOLUTIONS TO A BOUNDARY-VALUE PROBLEM FOR AN INFINITE SYSTEM OF DIFFERENTIAL EQUATIONS
Electronic Journal of Differential Equations, Vol. 217 (217, No. 262, pp. 1 12. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE OF SOLUTIONS TO A BOUNDARY-VALUE
More informationCONSEQUENCES OF TALENTI S INEQUALITY BECOMING EQUALITY. 1. Introduction
Electronic Journal of ifferential Equations, Vol. 2011 (2011), No. 165, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu CONSEQUENCES OF
More informationTail Approximation of the Skew-Normal by the Skew-Normal Laplace: Application to Owen s T Function and the Bivariate Normal Distribution
Journal of Statistical and Econometric ethods vol. no. 3 - ISS: 5-557 print version 5-565online Scienpress Ltd 3 Tail Approimation of the Skew-ormal by the Skew-ormal Laplace: Application to Owen s T Function
More informationA novel difference schemes for analyzing the fractional Navier- Stokes equations
DOI: 0.55/auom-207-005 An. Şt. Univ. Ovidius Constanţa Vol. 25(),207, 95 206 A novel difference schemes for analyzing the fractional Navier- Stokes equations Khosro Sayevand, Dumitru Baleanu, Fatemeh Sahsavand
More informationON THE OSCILLATION OF THE SOLUTIONS TO LINEAR DIFFERENCE EQUATIONS WITH VARIABLE DELAY
Electronic Journal of Differential Equations, Vol. 008(008, No. 50, pp. 1 15. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp ON THE
More informationSIMULTANEOUS AND NON-SIMULTANEOUS BLOW-UP AND UNIFORM BLOW-UP PROFILES FOR REACTION-DIFFUSION SYSTEM
Electronic Journal of Differential Euations, Vol. 22 (22), No. 26, pp. 9. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SIMULTANEOUS AND NON-SIMULTANEOUS
More informationLINEAR SECOND-ORDER EQUATIONS
LINEAR SECON-ORER EQUATIONS Classification In two independent variables x and y, the general form is Au xx + 2Bu xy + Cu yy + u x + Eu y + Fu + G = 0. The coefficients are continuous functions of (x, y)
More informationLONG TERM BEHAVIOR OF SOLUTIONS FOR RICCATI INITIAL-VALUE PROBLEMS
Electronic Journal of Differential Equations, Vol. 8(8, No. 4, pp. 8. ISSN: 7-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp LONG TERM BEHAVIOR
More informationEXISTENCE AND APPROXIMATION OF SOLUTIONS OF SECOND ORDER NONLINEAR NEUMANN PROBLEMS
Electronic Journal of Differential Equations, Vol. 2005(2005), No. 03, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) EXISTENCE
More informationASYMPTOTIC THEORY FOR WEAKLY NON-LINEAR WAVE EQUATIONS IN SEMI-INFINITE DOMAINS
Electronic Journal of Differential Equations, Vol. 004(004), No. 07, pp. 8. ISSN: 07-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) ASYMPTOTIC
More informationBOUNDARY-VALUE PROBLEMS FOR NONLINEAR THIRD-ORDER q-difference EQUATIONS
Electronic Journal of Differential Equations, Vol. 211 (211), No. 94, pp. 1 7. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu BOUNDARY-VALUE PROBLEMS
More informationSimple Examples on Rectangular Domains
84 Chapter 5 Simple Examples on Rectangular Domains In this chapter we consider simple elliptic boundary value problems in rectangular domains in R 2 or R 3 ; our prototype example is the Poisson equation
More informationAMS subject classifications. Primary, 65N15, 65N30, 76D07; Secondary, 35B45, 35J50
A SIMPLE FINITE ELEMENT METHOD FOR THE STOKES EQUATIONS LIN MU AND XIU YE Abstract. The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in
More informationTRIPLE POSITIVE SOLUTIONS FOR A CLASS OF TWO-POINT BOUNDARY-VALUE PROBLEMS
Electronic Journal of Differential Equations, Vol. 24(24), No. 6, pp. 8. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) TRIPLE POSITIVE
More informationDIFFERENTIAL EQUATIONS WITH A DIFFERENCE QUOTIENT
Electronic Journal of Differential Equations, Vol. 217 (217, No. 227, pp. 1 42. ISSN: 172-6691. URL: http://ejde.math.tstate.edu or http://ejde.math.unt.edu DIFFERENTIAL EQUATIONS WITH A DIFFERENCE QUOTIENT
More informationGREEN S FUNCTIONAL FOR SECOND-ORDER LINEAR DIFFERENTIAL EQUATION WITH NONLOCAL CONDITIONS
Electronic Journal of Differential Equations, Vol. 1 (1), No. 11, pp. 1 1. ISSN: 17-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu GREEN S FUNCTIONAL FOR
More informationON THE CAUCHY-PROBLEM FOR GENERALIZED KADOMTSEV-PETVIASHVILI-II EQUATIONS
Electronic Journal of Differential Equations, Vol. 009(009), No. 8, pp. 1 9. ISSN: 107-6691. URL: http://ejde.math.tstate.edu or http://ejde.math.unt.edu ftp ejde.math.tstate.edu ON THE CAUCHY-PROBLEM
More informationNONCLASSICAL SHOCK WAVES OF CONSERVATION LAWS: FLUX FUNCTION HAVING TWO INFLECTION POINTS
Electronic Journal of Differential Equations, Vol. 2006(2006), No. 149, pp. 1 18. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) NONCLASSICAL
More informationNumerical Solutions to Partial Differential Equations
Numerical Solutions to Partial Differential Equations Zhiping Li LMAM and School of Mathematical Sciences Peking University Numerical Methods for Partial Differential Equations Finite Difference Methods
More informationUNIQUENESS OF SELF-SIMILAR VERY SINGULAR SOLUTION FOR NON-NEWTONIAN POLYTROPIC FILTRATION EQUATIONS WITH GRADIENT ABSORPTION
Electronic Journal of Differential Equations, Vol. 2015 2015), No. 83, pp. 1 9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu UNIQUENESS OF SELF-SIMILAR
More informationLYAPUNOV STABILITY OF CLOSED SETS IN IMPULSIVE SEMIDYNAMICAL SYSTEMS
Electronic Journal of Differential Equations, Vol. 2010(2010, No. 78, pp. 1 18. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu LYAPUNOV STABILITY
More informationOn Estimates of Biharmonic Functions on Lipschitz and Convex Domains
The Journal of Geometric Analysis Volume 16, Number 4, 2006 On Estimates of Biharmonic Functions on Lipschitz and Convex Domains By Zhongwei Shen ABSTRACT. Using Maz ya type integral identities with power
More informationJournal of Mathematical Analysis and Applications
J. Math. Anal. Appl. 35 29) 276 282 Contents lists available at ScienceDirect Journal of Mathematical Analysis and Applications www.elsevier.com/locate/jmaa A Turán-type inequality for the gamma function
More informationarxiv: v1 [math.na] 29 Feb 2016
EFFECTIVE IMPLEMENTATION OF THE WEAK GALERKIN FINITE ELEMENT METHODS FOR THE BIHARMONIC EQUATION LIN MU, JUNPING WANG, AND XIU YE Abstract. arxiv:1602.08817v1 [math.na] 29 Feb 2016 The weak Galerkin (WG)
More informationMULTIPLE SOLUTIONS FOR CRITICAL ELLIPTIC PROBLEMS WITH FRACTIONAL LAPLACIAN
Electronic Journal of Differential Equations, Vol. 016 (016), No. 97, pp. 1 11. ISSN: 107-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu MULTIPLE SOLUTIONS
More informationGENERIC SOLVABILITY FOR THE 3-D NAVIER-STOKES EQUATIONS WITH NONREGULAR FORCE
Electronic Journal of Differential Equations, Vol. 2(2), No. 78, pp. 1 8. ISSN: 172-6691. UR: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) GENERIC SOVABIITY
More informationAn ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains
c de Gruyter 2009 J. Inv. Ill-Posed Problems 17 (2009), 703 711 DOI 10.1515 / JIIP.2009.041 An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domains W. Arendt and T. Regińska
More informationBLOW-UP OF SOLUTIONS FOR VISCOELASTIC EQUATIONS OF KIRCHHOFF TYPE WITH ARBITRARY POSITIVE INITIAL ENERGY
Electronic Journal of Differential Equations, Vol. 6 6, No. 33, pp. 8. ISSN: 7-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu BLOW-UP OF SOLUTIONS FOR VISCOELASTIC EQUATIONS OF KIRCHHOFF
More informationBoundary Value Problems of Complex Variables
Boundary Value Problems of Complex Variables Dissertation zur Erlangung des Doktorgrades (Dr.rer.nat.) des Fachbereichs Mathematik und Informatik der Freien Universität Berlin vorgelegt von Alip Mohammed
More informationRemarks on the analysis of finite element methods on a Shishkin mesh: are Scott-Zhang interpolants applicable?
Remarks on the analysis of finite element methods on a Shishkin mesh: are Scott-Zhang interpolants applicable? Thomas Apel, Hans-G. Roos 22.7.2008 Abstract In the first part of the paper we discuss minimal
More informationALEKSANDROV-TYPE ESTIMATES FOR A PARABOLIC MONGE-AMPÈRE EQUATION
Electronic Journal of Differential Equations, Vol. 2005(2005), No. 11, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) ALEKSANDROV-TYPE
More informationHARDY INEQUALITIES WITH BOUNDARY TERMS. x 2 dx u 2 dx. (1.2) u 2 = u 2 dx.
Electronic Journal of Differential Equations, Vol. 003(003), No. 3, pp. 1 8. ISSN: 107-6691. UL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) HADY INEQUALITIES
More informationNONLINEAR FREDHOLM ALTERNATIVE FOR THE p-laplacian UNDER NONHOMOGENEOUS NEUMANN BOUNDARY CONDITION
Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 210, pp. 1 7. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu NONLINEAR FREDHOLM ALTERNATIVE FOR THE p-laplacian
More informationTENSOR TRANSFORMATION OF STRESSES
GG303 Lecture 18 9/4/01 1 TENSOR TRANSFORMATION OF STRESSES Transformation of stresses between planes of arbitrar orientation In the 2-D eample of lecture 16, the normal and shear stresses (tractions)
More informationAN EXTENSION OF THE LAX-MILGRAM THEOREM AND ITS APPLICATION TO FRACTIONAL DIFFERENTIAL EQUATIONS
Electronic Journal of Differential Equations, Vol. 215 (215), No. 95, pp. 1 9. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu AN EXTENSION OF THE
More informationGROWTH OF SOLUTIONS TO HIGHER ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS IN ANGULAR DOMAINS
Electronic Journal of Differential Equations, Vol 200(200), No 64, pp 7 ISSN: 072-669 URL: http://ejdemathtxstateedu or http://ejdemathuntedu ftp ejdemathtxstateedu GROWTH OF SOLUTIONS TO HIGHER ORDER
More informationANALYSIS AND APPLICATION OF DIFFUSION EQUATIONS INVOLVING A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL
Electronic Journal of Differential Equations, Vol. 217 (217), No. 289, pp. 1 6. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ANALYSIS AND APPLICATION OF DIFFUSION EQUATIONS
More informationASYMPTOTIC PROPERTIES OF SOLUTIONS TO LINEAR NONAUTONOMOUS DELAY DIFFERENTIAL EQUATIONS THROUGH GENERALIZED CHARACTERISTIC EQUATIONS
Electronic Journal of Differential Equations, Vol. 2(2), No. 95, pp. 5. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu ASYMPTOTIC PROPERTIES OF SOLUTIONS
More informationMA8502 Numerical solution of partial differential equations. The Poisson problem: Mixed Dirichlet/Neumann boundary conditions along curved boundaries
MA85 Numerical solution of partial differential equations The Poisson problem: Mied Dirichlet/Neumann boundar conditions along curved boundaries Fall c Einar M. Rønquist Department of Mathematical Sciences
More informationInstitute of Mathematics, Russian Academy of Sciences Universitetskiĭ Prosp. 4, Novosibirsk, Russia
PARTIAL DIFFERENTIAL EQUATIONS BANACH CENTER PUBLICATIONS, VOLUME 27 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WARSZAWA 1992 L p -THEORY OF BOUNDARY VALUE PROBLEMS FOR SOBOLEV TYPE EQUATIONS
More informationINITIAL-VALUE PROBLEMS FOR FIRST-ORDER DIFFERENTIAL RECURRENCE EQUATIONS WITH AUTO-CONVOLUTION
Electronic Journal of Differential Equations, Vol (), No, pp 3 ISSN: 7-669 URL: http://ejdemathtxstateedu or http://ejdemathuntedu ftp ejdemathtxstateedu INITIAL-VALUE PROBLEMS FOR FIRST-ORDER DIFFERENTIAL
More informationPYRAMIDAL CENTRAL CONFIGURATIONS AND PERVERSE SOLUTIONS
Electronic Journal of Differential Equations, Vol. 2004(2004), No. 06, pp. 9. ISSN: 072-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) PYRAMIDAL
More informationChapter 3 Burgers Equation
Chapter 3 Burgers Equation One of the major challenges in the field of comple systems is a thorough understanding of the phenomenon of turbulence. Direct numerical simulations (DNS) have substantially
More informationTable of Contents. II. PDE classification II.1. Motivation and Examples. II.2. Classification. II.3. Well-posedness according to Hadamard
Table of Contents II. PDE classification II.. Motivation and Examples II.2. Classification II.3. Well-posedness according to Hadamard Chapter II (ContentChapterII) Crashtest: Reality Simulation http:www.ara.comprojectssvocrownvic.htm
More informationRobust Monolithic - Multigrid FEM Solver for Three Fields Formulation Rising from non-newtonian Flow Problems
Robust Monolithic - Multigrid FEM Solver for Three Fields Formulation Rising from non-newtonian Flow Problems M. Aaqib Afaq Institute for Applied Mathematics and Numerics (LSIII) TU Dortmund 13 July 2017
More informationMEAN VALUE THEOREM FOR HOLOMORPHIC FUNCTIONS
Electronic Journal of Differential Equations, Vol. 2012 (2012, No. 34, pp. 1 6. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu MEAN VALUE THEOREM
More informationNonexistence of solutions for quasilinear elliptic equations with p-growth in the gradient
Electronic Journal of Differential Equations, Vol. 2002(2002), No. 54, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) Nonexistence
More informationON THE HILBERT INEQUALITY. 1. Introduction. π 2 a m + n. is called the Hilbert inequality for double series, where n=1.
Acta Math. Univ. Comenianae Vol. LXXVII, 8, pp. 35 3 35 ON THE HILBERT INEQUALITY ZHOU YU and GAO MINGZHE Abstract. In this paper it is shown that the Hilbert inequality for double series can be improved
More informationPERIODIC SOLUTIONS FOR NON-AUTONOMOUS SECOND-ORDER DIFFERENTIAL SYSTEMS WITH (q, p)-laplacian
Electronic Journal of Differential Euations, Vol. 24 (24), No. 64, pp. 3. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu PERIODIC SOLUIONS FOR NON-AUONOMOUS
More information