Nguyet Minh Mach Curriculum Vitae Birth Email Personal Data 3 rd of July, 1985, Can Tho, Viet Nam minh.mach@helsinki.fi Phone +358 (0)44 956 1064 (mobile) Gender Nationality Work address Current position Female Vietnamese University of Helsinki Department of Mathematics and Statistics Room D312 (Exactum), P.O. Box 68 (Gustaf Hällströmin katu 2b) FI-00014, Helsinki, Finlad Postdoc, Department of Mathematics and Statistics, University of Helsinki Education 01.01.2009 31.07.2012 01.09.2003 30.06.2007 PhD in Mathematics, Università di Pisa, Italy, Advisor: Professor Giovanni Alberti. Thesis: Weak solutions to rate-independent systems: Existence and Regularity, defense on 31 July 2012. BS in Mathematics and Computer Sciences, Viet Nam National University at Ho Chi Minh City, Honor Program, Advisor: Professor Dang Duc Trong. Thesis: A nonlinear backward heat equation: Uniqueness, Regularization, and Error Estimates, defense on 10 July 2007. Awards and Scholarships 2009-2012 Galieo Galilei Scholarship, Università di Pisa 2007 Valedictorian of Viet Nam National University at Ho Chi Minh City Toshiba Scholarship for excellent undergraduate students 2003-2007 Scholarship of Viet Nam National University for excellent students 2006 AmCham Scholarship for excellent undergraduate students Lawrences Ting Memorial Fund Scholarship for outstanding students 2005 Third prize in Viet Nam Mathematical Olympiad for undergraduate students
2003 Odon Vallet Scholarship for outstanding high school students Third prize in Viet Nam Mathematical Olympiad for high school students 01.10.2016 now 01.10.2015 30.09.2016 01.11.2013 30.09.2015 01.10.2012 30.09.2013 01.07.2007 30.06.2008 Summer 2016 Winter 2015/2016 Summer 2015 Winter 2014/2015 Summer 2014 Winter 2013/2014 Work Experience Vocational Postdoc, Department of Mathematics and Statistics, University of Helsinki. Stroke EIT imaging Stability analysis for the anisotropic D-bar method Postdoc, Department of Mathematics, Goethe University Frankfurt. Shape reconstruction in electrical impedance tomography: applications for real data Postdoc, Department of Mathematics, University of Stuttgart. Developed a shape reconstruction algorithm in electrical impedance tomography with global convergence property. Postdoc, Archimedes Center for Modeling, Analysis and Computation, Department of Applied Mathematics, University of Crete. Quasi-static evolution as limit of dynamic processes. Miscellaneous Assistant Actuary, Prudential Vietnam Assurance Company Ltd. Pricing products and analyzing the actual data to forecast the risks and profitability. Teaching Experience Teaching Assistant for Numerics of Differential Equations (1 st -3 rd year student, Goethe University Frankfurt) Teaching Assistant for Regularization of Inverse Problems (Master s student, Goethe University Frankfurt) Matlab Vorkurs (1 st -3 rd year student, Goethe University Frankfurt) Analysis II for Engineers (2 nd year students, Uni- Teaching Assistant for versity of Stuttgart) Teaching Assistant for Analysis III for Engineers (3 rd year students, University of Stuttgart) Teaching Assistant for Numerical Methods for Differential Equations (Master s students, University of Stuttgart) Teaching Assistant for Modeling with Partial Differential Equations (3 rd year students, University of Stuttgart)
Teaching Assistant for Stuttgart) Linear Structure (1 st year students, University of
Research Experience I have been working on different aspects of partial differential equations which are motivated by applications, such as backward heat equations, rate-independent systems, the inverse conductivity equation and the Poisson-Nernst-Planck system. Backward heat equations: During my undergraduate, I studied backward heat equations, where a time-dependent solution of a parabolic partial differential equation is reconstructed upon the measurement of the solution at final time. This problem is severely ill-posed in the sense that a small error of data may cause a large error of solutions and some regularization theory is needed to make the numerical computation possible. We proposed a regularization scheme to recover the solution from initial conditions for an unknown heat source and extra information on part of the domain s boundary in 1-dim [2] and in 2-dim with Hölder-type convergence [3]; for a known locally Lipschitz heat source in finite-dimension [5], in a Hilbert space [7] and for time-fractional derivative in 2-dim [11]. Rate-independent systems (RIS): As a graduate student, I studied (abstract) RIS, which are a kind of time-dependent processes evolving through equilibrium positions. It is known that these systems do not admit classical solutions, and some special kinds of weak solutions such as energetic solutions and BV solutions are of interest. In [6] I introduced another construction of BV solutions, and in [4] I proved that in 1-dim the energetic and BV solutions are piecewise-differentiable under some appropriate assumptions. Inverse conductivity equation: In the last two years, I have been investigating the inverse conductivity equation, which is a mathematical model for several applications such as electrical impedance tomography, mine detection in geophysics, identifying cracks by non-destructive testing, etc. The inverse problem of recovering the spatially-dependent coefficient of an elliptic partial differential equation from the boundary values of solutions is nonlinear and severely ill-posed, and a small amounts of noise or model errors may cause poor spatial resolution. We have established in [8] a new regularization method to reconstruct this coefficient s contrast. This is the first method in this field that satisfies all of following properties: stability under high levels of noise, real-time implementation and rigorous global convergence property. Poisson-Nernst-Planck system (PNP): Very recently I have started to work on the PNP system, one of the commonly used models to describe the movements of ions across the cellular membrane through ion channels. In the PNP system, ions are understood as point particles without size. When ions are crowded in a narrow channel, the ion-size effect (steric effect) becomes essential. This results in the inaccuracy of the PNP system and new model which involves the steric effect is needed. Although there have been many works concerned with the PNP system, the existence of solutions to the PNP system with steric effect has not yet been established in the literature. By proving the equivalence between the PNP system and a system of differential algebraic equations, we are able to establish the existence of stationary solutions to the PNP system with steric effect [10].
Current Research Interests I am interested in analysis and partial differential equations. In particular, I focus on the following topics: Inverse Problems such as the inverse conductivity equation, the inverse spectral problems, the inverse scattering problems, the backward heat equations, the inverse source problems Rate-independent systems: existence and regularity of weak solutions, real-life applications The Poisson-Nernst-Planck system: existence, asymptotic behavior, numerical solutions Research Articles 12. with Nguyen Huy Tuan, Le Dinh Long and Mokhtar Kirane, On a backward problem for inhomogeneous time-fractional diffusion equation on the plane, In Preparation. 11. with Li-Chang Hung, Stationary solutions to the Poisson-Nernst-Planck equations with steric effect, submitted. 10. with Bastian von Harrach, Monotonicity-based regularization for phantom experiment data in Electrical Impedance Tomography, submitted. 9. with Nguyen Huy Tuan and Mokhtar Kirane, A backward parabolic problem with locally lipschitz source, submitted. 8. with Nguyen Huy Tuan, Vo Anh Khoa and Thanh Tran, Reconstruction of the electric field of the Helmholtz equation in three dimensions, Journal of Computational and Applied Mathematics, Volume 309, 1 January 2017, Pages 56 78. 7. with Bastian von Harrach, Enhancing residual-based techniques with shape reconstruction features in Electrical Impedance Tomography, Inverse Problems, 32 (2016) 125002 (21pp). 6. BV solutions constructed by epsilon-neighborhood method, ESAIM: COCV, 22(1),188-207, 2016. 5. with Dang Duc Trong and Bui Thanh Duy, Backward heat equations with locally lipschitz source, Applicable Analysis: An International Journal, 2014. 4. Regularity of solutions to nonconvex rate-independent systems in one-dimension, Math. Nachr., 1-22, 2014. 3. with Dang Duc Trong, Pham Ngoc Dinh Alain and Phan Thanh Nam, Hölder-type approximation for the spatial source term of a backward heat equation, Numer. Funct. Anal. Optim., 31(12), 2010. 2. with Dang Duc Trong and Phan Thanh Nam, Recovering a class of entire functions and application to heat equations, Vietnam J. Math., 37, 2009. 1. with Phan Thanh Nam, Proof of a conjecture on general means, JIPAM J. Inequal. Pure Appl. Math., 9, 2008. May 2017 Apr 2017 Oct 2016 Talks Applied Inverse Problems Conference, Zhejiang University, China Workshop on Numerical Methods for Optimal Control and Inverse Problems, Technische Universität München, Germany Inverse Problems Seminar, Department of Mathematics and Statistics, University of Helsinki, Finland
Aug 2016 Mar 2016 Mar 2016 Mar 2016 May 2015 Jul 2014 May 2013 Dec 2012 Conference on Multiscale Inverse Problems, Loka Brunn, Sweden Workshop on Inverse Problems for PDEs, University of Bremen, Germany Workshop on Numerical Methods for Optimal Control and Inverse Problems, Technische Universität München, Germany Joint annual meeting of the GAMM & DMV, Technische Universität Braunschweig, Germany Applied Inverse Problems Conference, University of Helsinki, Finland Summer Program on "PDEs and Applied Mathematics", VIASM, Vietnam Pure and Applied Mathematics Seminar, Department of Mathematics and Statistics, University of Cyprus, Cyprus Applied and Numerical Analysis Seminar, Department of Applied Mathematics, University of Crete, Greece Reviewing & Refereeing 2014-now 2014-now Reviewer for Mathematical Reviews, Zentralblatt MATH Referee for journals: J. Math. Inequal., Math. Methods Appl. Sci., Computers & Mathematics with Applications, Inverse Problems in Science & Engineering References Professor Giovanni Alberti, Università di Pisa, Ph.D. Advisor Email: galberti1@dm.unipi.it Professor Bastian von Harrach, Goethe-Universität Frankfurt am Main, Supervisor Email: harrach@math.uni-frankfurt.de Professor Matti Lassas, University of Helsinki, Supervisor Email: matti.lassas@helsinki.fi Professor Samuli Siltanen, University of Helsinki, Supervisor Email: samuli.siltanen@helsinki.fi Professor Riccarda Rossi, University of Brescia Email: riccarda.rossi@ing.unibs.it