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Mai Đức Thành

Mai Đức Thành
Mai Đức Thành
Assoc. Prof. Dr.
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Assoc. Prof. Dr.
Office: A2.610
Telephone: 08.37244270
E-mail: mdthanh@hcmiu.edu.vn
  • Ph.D. in Numerical Analysis, Ecole Polytechnique de Paris, France, 2000 - 2003;

Advisor: Philippe G. LeFloch

  • M.Sc. in Numerical Analysis, Ecole Polytechnique de Paris, France, 1999 - 2000;
  • B.Sc. in Mathematics,  Pedagogical University of Hue, Vietnam, 1991-1995.

Permanent:

  • Associate Professor, International University, Vietnam National University-Ho Chi Minh City, from 2010
  • Assistant Professor,  International University, Vietnam National University-Ho Chi Minh City, 2005-2010
  • Assistant Professor, University of Technology, Vietnam National University-Ho Chi Minh City, 2004-2005
  • Researcher, Hanoi Institute of Mathematics,  Vietnamese Academy of Science and Technology, 1995-2004

Visiting:

  • Visiting lecturer, LAGA, University of Paris 13, May 2005
  • Postdoc, Institute of Applied Mathematics, University of Freiburg, Germany, 2003-2004. Host: D. Kroener.
  • Visiting scolar, Department of Mathematics, University of Houston, Texas, June 2004
  • Visiting, Center for Risk Study and Safety, University of California, Santa Barbara, May 2004
  • Visiting, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, February-March 2003
  • Visiting, CEMRACS, Luminy, France, July-August 1999
  • Visiting, ICTP, Trieste, Italy, September-October 2006
  • Membership: American Mathematical Society (AMS), Vietnamese Mathematical Society
  • Reviewer  of  Mathematical Reviews,  AMS
  • Referee of Journals:   SIAM J. Mathematical Analysis, SIAM J. Scientific Computing,  Mathematical Analysis & Applications, Computational & Applied Mathematics, Applied Mathematics & Computation, Vietnam J. Mathematics, Numerische Mathematik, Journal of Hyperbolic Differential Equations

Ph.D. Students:

  1. Dao Huy Cuong
  2. Nguyen Huu Hiep

Master Students:

  1. Nguyen Ngoc Tien
  2. Ho Dac Nghia
  3. Nguyen Hoang Quan
  4. Phan Thanh Tam
  5. Doan Vu Ngoc Hien
  6. Pham Viet Thanh
  7. Nguyen Huu Hiep
  8. Dao Huy Cuong
  9. Phan Cao Dat
  10. Thach Phuoc
  11. Mai Thi Hong
  12. Nguyen Ai Nguyen

Research Fields: Numerical Analysis, 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
  •  Applications to multiphase flow models
  1. M.D. Thanh and D.H. Cuong, Existence of solutions to the Riemann problem for a model of two-phase  flows, Elect. J. Diff. Eqs., Vol. 2015 (2015), No. 32, pp. 1-18.
  2. D.H. Cuong and M.D. Thanh, A Godunov-type scheme  for the isentropic model of a fluid flow in a nozzle with variable  cross-section, Appl. Math. Comput., http://dx.doi.org/10.1016/j.amc.2015.01.024
  3. M.D. Thanh, N.H. Hiep, Existence of traveling waves to any Lax shock satisfying Oleinik's criterion in conservation laws, Appicable Anal.,DOI:10.1080/00036811.2014.915520
  4. M.D. Thanh, A phase decomposition approach and the Riemann problem for a model of two-phase flows, J. Math. Anal. Appl,. 418 (2014), pp. 569-594.
  5. M.D. Thanh and D.Kroener, Testing improvements of a well-balanced method for the model of a fluid in a nozzle with variable cross-section, Taiwan. J. Math., DOI: 10.11650/tjm.18.2014.4092
  6. M.D. Thanh, N.H. Hiep, On traveling waves in  viscous-capillary Euler equations with thermal conductivity, Appl. Math. Comput., 234C (2014), pp. 127-141
  7. M.D. Thanh, Building fast well-balanced two-stage numerical schemes  for a model of two-phase flows, Commun. Nonl. Sci. Num. Simulat., 19 (2014) 1836–1858
  8. M.D. Thanh, D.H. Cuong, Properties of the wave curves in the shallow water equations with discontinuous topography, Bull. Malays. Math. Sci. Soc., (accepted for publication).  
  9. M.D. Thanh, N.D. Huy, N.H. Hiep, D.H. Cuong, Existence of  traveling waves in van der Waals fluids with viscosity and capillarity effects, Nonlinear Analysis: TMA, 95 (2014), 743–755.
  10. M.D. Thanh, Well-balanced  Roe-type numerical scheme for a model of two-phase compressible flows, J. Korean Math. Soc. 51 (2014), No. 1, pp. 163-187
  11. M.D. Thanh, Remarks on traveling waves and equilibria in fluid dynamics with viscosity, capillarity, and heat conduction, Nonlinear Analysis: RWA, 16 (2014) 40–47
  12. M.D. Thanh, Numerical treatment in resonant regime for shallow water equations with discontinuous topography, Commun. Nonl. Sci. Num. Simulat., 18 (2013) 417–433
  13. M.D. Thanh, D. Kroener, Numerical treatment of nonconservative terms in resonant regime for fluid flows in a nozzle with variable cross-section, Computers & Fluids, 66 (2012), 130–139
  14. M.D. Thanh, D. Kroener, C. Chalons, A robust numerical method for approximating solutions of a model of two-phase flows and its properties, Appl. Math.  Comput., 219 (2012) 320-344
  15. M.D. Thanh, Existence of traveling waves in compressible Euler  equations with viscosity and capillarity, Nonlinear Analysis: TMA 75 (2012), 4884-4895
  16. M.D. Thanh, Exact solutions of a two-fluid model of two-phase compressible flows with gravity, Nonlinear Analysis: RWA 13 (2012), 987-998
  17. 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
  18. 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
  19. 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
  20. M.D. Thanh, Remarks on nonclassical shock waves for Van der Waals fluids, Acta Math. Viet., Volume 36, Number 2, (2011), 451-468
  21. M.D. Thanh, Traveling waves   of an elliptic-hyperbolic model of phase transitions via varying viscosity-capillarity, J. Differential Equations 251 (2011), 439-456.
  22. 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.
  23. M.D. Thanh, Existence of traveling waves in elastodynamics with variable viscosity and capillarity, Nonlinear Analysis: RWA 12 (2011), 236-245. 
  24. M.D. Thanh, Attractor and traveling waves of a fluid with nonlinear diffusion and dispersion,  Nonlinear Analysis: TMA  72 (2010), 3136-3149.
  25. M.D. Thanh, Global existence of diffusive-dispersive traveling waves for general flux functions, Nonlinear Analysis: TMA  72 (2010),  231-239
  26. M.D. Thanh, The Riemann problem for a non-isentropic fluid in a nozzle with discontinuous cross-sectional area, SIAM J. Appl. Math. 69 (2009) ,1501—1519.
  27. M.D.Thanh and A.Izani Md. Ismail, Well-balanced scheme for a one-pressure model of two-phase flows, Physica Scripta, 79, 2009.
  28. 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
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35.  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.
  36. 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.
  37.  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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42.  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
  43. 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
  44. 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