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Assoc.Prof. Dr. Mai Duc Thanh
E-mails: mdthanh@hcmiu.edu.vn
Telephone: +84-8-72 42 181 (Ext 3311)
Fax: +84-8-72 42 195
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Education
- 2000 – 2003 : Ph.D. degree in Numerical Analysis, Ecole Polytechnique de Paris, France.
Advisor: Philippe G. LeFloch
- 1999 -- 2000 : Master degree in Numerical Analysis, Ecole Polytechnique de Paris, France.
- 1991-1995: B.Sc. degree in Math: Pedagogical University of Hue, Vietnam.
Research Interests
Research Fields: Numerical Analysis and Partial Differential Equations.
Research Themes:
- Mathematical Analysis of shock waves in hyperbolic systems of balance laws
- Traveling waves in diffusive-dispersive models
- Numerical approximations for systems of balance laws
Career
- From 2010--: Associate Professor, International University-VNU HCM
- From 2005--2010: Assistant Professor, International University-VNU HCM
- From 2004--2005: Assistant Professor, University of Technology-VNU HCM
- 9/2003—8/2004: Postdoc, Institute of Applied Mathematics, University of Freiburg, Germany. Host: Prof. D. Kröner
- 1995—2004: Researcher, Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology
- Awarded Dong Luan prize 2009
- Membership: American Mathematical Society (AMS), Vietnamese Mathematical Society
- Reviewer of Mathematical Reviews, AMS
- Referees of International Journals: SIAM J. Scientific Computing, Mathematical Analysis & Applications, Computational &Applied Mathematics, Applied. Mathematics & Computations, Vietnam J. Mathematics, Numerische Mathematik, Journal of Hyperbolic Differential Equation
Teaching
- Calculus
- Discrete Mathematics
- Numerical Methods
- Ordinary Differential Equations
- Partial Differential Equations
- Hyperbolic Systems of Conservation Laws
Publications
- M.D. Thanh, Existence of traveling waves in compressible Euler equations with viscosity and capillarity, Nonlinear Analysis: TMA, DOI:10.1016/j.na.2012.04.003
- M.D. Thanh, Exact solutions of a two-fluid model of two-phase compressible flows with gravity, Nonlinear Analysis: RWA, 13 (2012), 987-998
- M.D. Thanh, On a two-fluid model of two-phase compressible flows and its numerical approximation, Commun. Nonlinear Sci. Numer. Simulat., 17 (2012) 195–211
- M.D. Thanh, Existence of traveling waves of conservation laws with singular diffusion and nonlinear dispersion, Bull. Malays. Math. Sci. Soc. 35 (2012), 383-398
- P.G. LeFloch and M.D. Thanh, A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime, J. Comput. Physics, 230 (2011) 7631–7660
- M.D. Thanh, Remarks on nonclassical shock waves for Van der Waals fluids, Acta Math. Viet., Volume 36, Number 2, (2011), 451-468
- M.D. Thanh, Stationary waves of a two-fluid model of two-phase compressible flows and their computations, Proc. Inter. Conf. Anal & Appl. Math., Sai Gon University, Ho Chi Minh City, March 2011, 205-221.
- M.D. Thanh, Traveling waves of an elliptic-hyperbolic model of phase transitions via varying viscosity-capillarity, J. Differential Equations, volume 251, number 2, (2011), 439-456.
- M.D. Thanh, D. Kröner, and N.T. Nam, Numerical approximation for a Baer-Nunziato model of two-phase flows., Appl. Numer. Math. 61 (2011), 702-721.
- M.D. Thanh, Existence of traveling waves in elastodynamics with variable viscosity and capillarity, Nonlinear Analysis: RWA, 12 (2011), 236-245.
- M.D. Thanh, Attractor and traveling waves of a fluid with nonlinear diffusion and dispersion, Nonlinear Analysis: TMA, Volume 72, Number 6, 3136-3149, 2010.
- M.D. Thanh, Global existence of diffusive-dispersive traveling waves for general flux functions, Nonlinear Analysis: TMA, Volume 72, Number 1, 231-239, 2010
- M.D. Thanh, The Riemann problem for a non-isentropic fluid in a nozzle with discontinuous cross-sectional area, SIAM J. Appl. Math., 69(6),1501—1519, 2009.
- M.D.Thanh and A.Izani Md. Ismail, Well-balanced scheme for a one-pressure model of two-phase flows, Physica Scripta, 79, 2009.
- A. Izani Md. Ismail, Md. Fazlul K., and M.D. Thanh, Tsunami Modelling using the Well-Balanced Scheme, Int. J. Math. Phys. & Engin. Sci., 2, 166-169
- D. Kröner, P.G. LeFloch, and M.D. Thanh, The minimum entropy principle for fluid flows in a nozzle with discontinuous cross-section, Math. Model. & Num. Anal., 42 (2008), 425-442.
- M.D. Thanh, Md. Fazlul K. and A. Izani Md. Ismail, Well-balanced scheme for shallow water equations with arbitrary topography, Inter. J. Dyn. Sys. and Diff. Eqs. Vol 1(3), 2008, 196-204.
- P.G. LeFloch and M.D. Thanh, The Riemann problem for shallow water equations with discontinuous topography, Com. Math. Sci., 5(4), (2007) 865-885.
- H.D. Nghia and M.D. Thanh, Nonclassical shock waves of conservation laws: flux-function having two inflection points, Elect. J. Diff, Eqs, Vol 2006, No 149, pages 1-17.
- D. Kröner and M.D. Thanh, A well-balanced numerical method for several models of two-phase flows, Proceedings of International Conference on Nonlinear Analysis & Engineering Mechanics Today, 2006, 90-115.
- D. Kröner and M.D. Thanh, On the model of a compressible flow in a nozzle: Analysis and Numerical Methods, Proc. Tenth. Intern. Conf. "Hyperbolic Problem: Theory, Numerics, and Applications", Osaka (2004), Yokohama Publishers, 117-124, 2006.
- D. Kröner and M.D. Thanh, Numerical solutions to compressible flows in a nozzle with variable cross-section, SIAM J. Numer. Anal. 43(2), (2005) 796—824.
- T. Pham Dinh, C. Rohde, and M.D. Thanh, A variational approach for approximating solutions to phase transition dynamics via time discretization, Proc.MCO’04, Hermes Edition, (2004), 383-391.
- C. Rohde and M.D. Thanh, Global existence for phase transition problems via a variational scheme, J. Hyp. Diff. Eqs., 1(4) (2004), 747-768.
- P.G. LeFloch and M.D. Thanh, The Riemann problem for fluid flows in a nozzle with discontinuous cross-section, Comm. Math. Sci., 1(4) 2003, 763-797.
- P.G. LeFloch and M.D. Thanh, Properties of Rankine-Hugoniot curves for Van der Waals fluid flows, Japan J. Indus. & Appl. Math., 20 (2), (2003), 211-238.
- P.G. LeFloch and M.D. Thanh, Non-classical Riemann solvers and kinetic relations. II. An hyperbolic-elliptic model of phase-transition dynamics, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 1, 181--219.
- T.D. Van, M.D. Thanh and N.H. Tho, On-Lax-Oleinik-type formulas for weak solution to scalar conservation laws, Viet. J. Math., 30 (2002), 193-198.
- J.M. Correia, P.G. LeFloch and M.D. Thanh, Hyperbolic Systems of Conservation Laws with Lipschitz Flux-Functions: the Riemann Problem, Bol. Soc. Brasil Mat., 32 (2001), No. 3, 271-301.
- T.D. Van and M.D. Thanh, On Representation of viscosity solutions to nonconvex-nonconcave Hamilton-Jacobi equations, Acta Math. Viet., 26 (2001), 395-405.
- P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. I. A nonconvex hyperbolic model of phase transitions, Z. Angew. Math. Phys. 52 (2001), no. 4, 597--619.
- P.G. LeFloch and M.D. Thanh, Nonclassical Riemann solvers and kinetic relations. III. A nonconvex hyperbolic model for van der Waals fluids, Electron. J. Diff. Equations, vol. 2000, No. 72, 19 pp
- T.D. Van and M.D. Thanh, The Oleinik-Lax-type Formulas for Multi-time Hamilton-Jacobi Equations, Adv. Math. Sci. Appl., 10 (2000), no. 1, 239--264
- T.D. Van, M.D. Thanh and R. Gorenflo, A Hopf-Type Formula for ut + H(t,u,Du)=0, Viet. J. Math., 26 (1998), no. 4, 385—389
- T.D. Van, M.D. Thanh, and N. Hoang, On the representation of Lipschitz global solutions of the Cauchy problem for Hamilton-Jacobi equations. Proc. Conf. Analysis and mechanics of continuous media (Ho Chi Minh City, 1995), 428--436.
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