Curriculum Vitae (Summary)

Transcription

1 Curriculum Vitae (Summary) Hermano Frid -Neto Personal Informations NAME NATIONALITY Hermano Frid -Neto Brazilian BIRTH June 10, 1958 PLACE Rio de Janeiro CIVIL STATUS Divorced; 1 daughter born 05/30/1986 PARENTS Armando Pereira Frid & Nice de Almirante Frid EDUCATION Undergraduate Course of Electronics Engeneering Military Institute of Engeneering IME (incomplete) Bachelor in Mathematics, Institute of Mathematics of the Federal University of Rio de Janeiro-UFRJ Master in Mathematics, Institute of Pure and Applied Mathematics IMPA 1

2 PhD, Institute of Pure and Applied Mathematics IMPA Professional Experience 04/2005-present Titular Researcher, Institute of Pure and Applied Mathematics-IMPA 02/ /2005 Associate Researcher, 1 Institute of Pure and Applied Mathematics-IMPA 01/ /2001 Visiting Faculty, Northwestern University, USA /2000 Associate Professor 4, 09/ /1996 Visiting Scholar, Northwestern University, USA Associate Professor 3, Associate Professor 2, Associate Professor 1, 08/ Assistant Professor 1, Assistant of Research, Institute of Pure and Applied Mathematics IMPA 1 According to the law regulating the carrier of researchers employed by the Brazilian Ministery of Science and Tecnology, promotion to Titular has a minimum delay of 5 years since the admittance. 2

3 Main Areas of Research: Theory of Nonlinear Systems of Conservation Laws. Nonlinear Partial Differential Equations in Fluid Mechanics. Geometric Measure Theory and Applications to Nonlinear PDE s Nonlinear Analysis Theses Advised 1991 Marcelo M. Santos, PhD Thesis, IMPA, 2 2 Non-strictly Hyperbolic Systems of Conservation Laws: The Cauchy Problem Leonardo Rendon, PhD, IM-UFRJ, Systems of Conservation Laws with Non-Lipschitz Flux Functions Cezar Issao Kondo, PhD, IM-UFRJ, Initial- Boudary Value Problems for One-Dimensional Systems of Conservation Laws in Noncylindrical Domains Wladimir Augusto das Neves, PhD, IM-UFRJ, Scalar Multidimensional Conservation Laws IBVP in Noncylindrical Lipschitz Domains Jean Carlos da Silva, IMPA, Multiscale Young Measures in Stochastic Homogenization with Applications to Nonlinear PDE s. 3

4 Activities as Referee, Reviewer and Consultant Has acted as referee of articles submitted to journals such as Transactions of the American Mathematical Society, Journal of Differential Equations, Nonlinearity, The Royal Society of Edinburgh Proceedings A (Mathematics), Journal of the London Mathematical Society, Indiana University Mathematics Journal, Contemporary Mathematics AMS, Electronic Journal of Differential Equations, Bulletin of the Brazilian Mathematical Society, and Matemática Contemporânea SBM. Has acted regularly as reviewer of the Mathematical Reviews, of the American Mathematical Society. Has acted regularly as ad hoc consultant for CNPq, CAPES, FAPERJ and FAPESP, agencies supporting research in Brazil, Rio de Janeiro and São Paulo. Member of the Mathematics and Statistics Commitee of CAPES for Evaluation of the Post-Graduation Courses of Brazil, in 1998 and Research Fellowships 01/2001-present 01/2006-present Fellowship award Scientists of the State of Rio de Janeiro, FAPERJ Research Fellowship, CNPq, Level 1A 08/ /2005 Research Fellowship, CNPq, Level 1B 08/ /1998 Research Fellowship, CNPq, Level 1C 09/ /1996 Post-Doctoral Fellowship, CNPq, in the Northwestern University, Evanston, Illinois, USA Research Fellowship, CNPq, Level 2A Research Fellowship, CNPq, Level 2B Research Fellowship, CNPq, Level 2C 4

5 Articles Published in Refereed Journals [1] The Morse index theorem for elliptic problems with a constant, Anais da Academia Brasileira de Ciências 55, no. 1 (1983), 9 10, with F. J. Thayer. [2] Lax Pairs, Boletim da Sociedade Brasileira de Matemática 15, no. 1&2 (1984), 1 6, with F. J. Thayer. [3] A stability theorem for entropy solutions to quasilinear hyperbolic systems in several space variables, Boletim da Soc. Bras. Mat. 19, no.1 (1988), [4] Uniqueness of solutions to hyperbolic balance laws in several space variables, Comm. Partial Diff. Eqs. 14, no. 8&9 (1989), [5] An abstract version of the Morse index theorem and its application to hypersurfaces with constant mean curvature, Boletim da Soc. Bras. Mat., Nova Série 20, no. 2 (1990), 59 68, with F. J. Thayer. [6] On a nonlinear hyperbolic problem arising in two-phase flow in naturally fractured reservoirs, Acta Applicandae Mathematicae 25 (1991), [7] The Cauchy problem for a class of nonstrictly hyperbolic systems of conservation laws, Matemática Contemporânea 3 (1992), 29 50, with M. M. Santos. [8] The Cauchy problem for the systems t z + x ( z γ ) = 0, J. Diff. Eqs. 111, no. 2 (1994), , with M. M. Santos. [9] Nonstrictly hyperbolic systems of conservation laws of conjugate type, Comm. Partial Diff. Eqs. 19, no. 1&2 (1994), 27 59, with M. M. Santos. [10] Solution to the initial-boundary value problem for the regularized Buckley- Leverett system, Acta Applicandae Mathematicae 38 (1995), [11] Measure-valued solutions for multiphase flow in porous media: existence and asymptotic steadiness of water flooding, Matemática Contemporanea 8 (1995), [12] Initial boundary value problems for systems of conservation laws, J. Diff. Eqs. 128, No.1 (1996), [13] Existence and asymptotic behavior of measure-valued solutions for threephase flow in porous media, J. Math. Anal. Appl., 196 (1995), [14] Invariant regions under difference schemes for conservation laws, Discrete and Continuous Dynamical Systems 1, 4 (1995), [15] Oscillation waves in Riemann problems inside elliptic regions for systems of mixed type, Z angew Math Phys ZAMP (J. Appl. Math. Phys.) 46 (1995), , with I-Shih Liu. [16] Oscillation waves in Riemann problems for phase transitions, Quaterly of Appl. Math. 56, No. 1, (1998), , with I-Shih Liu. 5

6 [17] Phase mixtures in dynamics of pseudoelasticity, Continuum Mechanics and Thermodynamics 7, No.4 (1995), , with I-Shih Liu. [18] Phase transitions and oscillation waves in an elastic bar, Matemática Contemporânea, 10 (1996), , with I-Shih Liu. [19] Measure-valued solutions to initial-boundary value problems for certain systems of conservation laws: existence and dynamics, Trans. Amer. Math. Soc., 348 (1996), [20] Existence and asymptotic behavior of the measure-valued solutions for degenerate conservation laws, J. Diff. Eqs. 127 (1996), , with G.-Q. Chen. [21] On a new concept of asymptotic stability for Riemann solutions, Matemática Contemporânea, 10 (1996), [22] Asymptotic decay of solutions to conservation laws, C. R. Acad. Sci. Paris, Serie I (1996), ; with G.-Q. Chen. [23] Asymptotic stability of Riemann waves for conservation laws, Z angew Math Phys ZAMP, 48 (1997), 30 44; with G.-Q. Chen. [24] Large-Time Behavior of Entropy Solutions of Conservation Laws, Journal of Differential Equations, 152 (1999), , with G.-Q. Chen. [25] Large-time behavior of entropy solutions in L for multidimensional scalar conservation laws, In: Advances in Nonlinear Partial Differential Equations and Related Areas, pp , G.-Q. Chen et al (eds.), World Scientific: Singapore, 1998, with G.-Q. Chen. [26] Decay of entropy solutions of nonlinear conservation laws, Arch. Rat. Mech. Anal. 146 (1999), ; with G.-Q. Chen. [27] On the Compressible Euler Equations in Thermoelasticity, Matemática Contemporânea, Brazilian Mathametical Society SBM, 15 (1998), 67 86, with G.-Q. Chen. [28] On the asymptotic behavior of solutions of certain multi-d systems of conservation laws, In: Hyperbolic Problems: Theory, Numerics, Applications, Seventh International Conference in Zürich, February 1998; Edited by M. Fey and R. Jeltsch. International Series of Numerical Mathematics 128, Birkhäuser, [29] Vanishing viscosity limit for initial-boundary value problems for conservation laws, Contemporary Mathematics 238 (1999), 35 51, with G.-Q. Chen. [30] Divergence-measure fields and conservation laws, Arch. Rat. Mech. Analysis 147 (1999), , with G.-Q. Chen. [31]Vanishing shear viscosity in the equations of compressible fluids for the 6

7 flows with the cylinder symmetry, accepted for publication in SIAM Journal of Mathematical Analysis (1999), with V. Shelukhin. [32]On boundary layers for the Navier-Stokes equations of compressible fluids, Comm. Math. Phys. 208 (1999), , with V. Shelukhin. [33] Uniqueness and Asymptotic Stability of Riemann solutions for the compressible Euler equations, Trans. American Math. Society 353 (2001), no.3, Joint with G.-Q. Chen. [34] Periodic solutions of conservation laws constructed through Glimm scheme, Transactions of the American Mathematical Society 353, No. 11 (2001), [35] Maps of convex sets and invariant regions for finite difference conservation laws, Archive for Rational Mechanics and Analysis 160 (2001), [36] Decay of almost periodic solutions of conservation laws, Archive for Rational Mechanics and Analysis 161 (2002), [37] Periodic and almost periodic solutions of conservation laws: global existence and decay. Boletim da Sociedade Brasileira de Matemática, 32, No. 1 (2001), [38] Uniqueness and stability of Riemann solutions with large oscilation in gas dynamics. Comm. Math. Phys., 228 (2002) 2, Jointly with G.-Q. Chen and Y. Li. [39] On the theory of divergence-measure fields and its applications. Boletim da Sociedade Brasileira de Matemática, 32, No. 3 (2001), Jointly with G.-Q. Chen. [40] On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of pressure filtration. SIAM Journal Math. Anal., 34 (2003) 3, Jointly with R. Buerger and K.H. Karlsen. [41] A quasilinear parabolic system for three-phase capillary flow in porous media. SIAM Journal Math. Anal., 35 (2003) 4, Joint with V. Shelukhin. [42] Extended divergence-measure fields and the Euler equations for gas dynamics. Communications in Mathematical Physics 236 (2003) 2, Joint with G.-Q. Chen. [43] Global stability of steady solutions for a model in virus dynamics. M2AN Math. Model. Numer. Anal. 37 (2003), no. 4, Joint with P.-E. Jabin and B. Perthame. [44] Correction to: Maps of convex sets and invariant regions for finitedifference systems of conservation laws [Arch. Ration. Mech. Anal

8 (2001), no. 3, ]. Arch. Ration. Mech. Anal. 171 (2004), no. 2, [45] Boundary layer in parabolic perturbations of scalar conservation laws. Z. Angew. Math. Phys.-ZAMP 55 (2004), no. 3, Jointly with V. Shelukhin. [46] Asymptotic stability of Riemann solutions for a class of multi-d viscous systems of conservation laws. Arch. Rat. Mech. Anal. 181 (2006), no.1, [47] Asymptotic stability of non-planar Riemann solutions for multi-d systems of conservation laws with symetric nonlinearities. J. Hyperbolic Differ. Equ. 1 (2004), no. 3, [48] Spatially periodic solutions in relativistic isentropic gas dynamics. Comm. Math. Phys. 250 (2004), no. 2, Jointly with M. Perepelitsa. [49] Initial boundary value problems for a quasilinear parabolic system in three-phase capillary flow in porous media. SIAM J. Math. Anal. 36 (2005), no.5, Jointly with V. Shelukhin. [50] Radially symmetric weak solutions for a quasilinear wave equation in two space dimensions. J. Diff. Eqs. 219 (2005), no.2, Joint with J.-P. Dias. [51] Finite difference schemes with cross derivatives correctors for multidimensional parabolic systems. J. Hyperbolic Differ. Equ. 3 (2006), no.1, Joint with F. Bouchut. [52]Uniqueness for multidimensional hyperbolic systems with commuting Jacobians. Arch. Rational Mech. Anal. 182 (2006), no.1, Joint with P.G. LeFloch. [53] Neumann problems for quasilinear parabolic systems modelling polydisperse suspensions. SIAM J. Math. Anal. 38 (2006), no.2, Jointly with S. Berres and R. Bürger. [54] Asymptotic stability of Riemann solutions in BGK approximations to certain multidimensional systems of conservation laws. J. Differential Equations 230 (2006), no.2, Joit with Leonardo Rendn. [55] On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition. J. Math. Anal. Appl. 326 (2007), no.1, Joint with Raimund Brger and Kenneth H. Karlsen. [56] L 1 Stability of spatially periodic solutions in relativistic gas dynamics. Communications in Mathematical Physics 284 (2008), no. 2, Jointly with D. Calvo and R. Colombo. 8

9 [57] Multiscale Young measures in almost periodic homogenization and applications. Archive for Rational Mechanics and Analysis 192 (2009), no. 1, (2008). Jointly with Luigi Ambrosio. [58] Nonlinear maps of convex sets in Hilbert spaces with application to kinetic equations. Bulletin of the Brazilian Mathematical Society (N.S.) 39 (2008), no. 3, (2008). [59] Multiscale Young measures in homogenization of continuous stationary processes in compact spaces and applications. Journal of Functional Analysis 256 (2009), no. 6, Jointly with L. Ambrosio and J.C. Silva. [60] Vanishing viscosity with short wave long wave interactions for systems of conservation laws. To appear in Archive for Rational Mechanics and Analysis (submitted, Dec. 2007; accepted, Mar. 2009). Joint with J.-P. Dias and M. Figueira. Books. [1] Compacidade Compensada Aplicada às Leis de Conservação; Notas de Curso do 19o Colóquio Brasileiro de Matemática, IMPA, RJ, [2] Partial Regularity of Solutions of the 3-D Incompressible Navier-Stokes Equations, Notas de Curso do 23o. Colóquio Brasileiro de Matemática, IMPA, Jointly with M. Perepelitsa. Recent Works. [1] Homogenization of nonlinear PDE s in the Fourier-Stieltjes algebras. Submitted (2008). Jointly with J.C. Silva. 9