## IU Web Directory

Name: Mai Duc Thanh

Position: Associate Professor

Department: Department of Mathematics

Title: Assoc. Prof. Dr.

Office: A2.610

Telephone: 08.37244270

E-mail:
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- 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

**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

__Some Scientific Activities__:

- 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

**Articles published in International Journals**:

- 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. - 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 - 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 - 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. - 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 - 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 - 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 - 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). - 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. - 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 - 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 - M.D. Thanh, Numerical treatment in resonant regime for shallow water equations with discontinuous topography
*, Commun. Nonl. Sci. Num. Simulat*., 18 (2013) 417–433 - 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 - 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 - M.D. Thanh, Existence of traveling waves in compressible Euler equations with viscosity and capillarity,
*Nonlinear Analysis: TMA*75 (2012), 4884-4895 - 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, Traveling waves of an elliptic-hyperbolic model of phase transitions via varying viscosity-capillarity
*, J. Differential Equations*251 (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*72 (2010), 3136-3149. - M.D. Thanh, Global existence of diffusive-dispersive traveling waves for general flux functions,
*Nonlinear Analysis: TMA*72 (2010), 231-239 - 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. - 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, Numerical solutions to compressible flows in a nozzle with variable cross-section,
*SIAM J. Numer. Anal*. 43(2), (2005) 796—824. - 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 u
_{t}+ H(t,u,Du)=0,*Viet. J. Math*., 26 (1998), no. 4, 385—389

I am Advisor of these students for their thesis.

**Ph.D. Students:**

Dao Huy Cuong

Nguyen Huu Hiep

**Master Students:**

Nguyen Ngoc Tien

Ho Dac Nghia

Nguyen Hoang Quan

Phan Thanh Tam

Doan Vu Ngoc Hien

Pham Viet Thanh

Nguyen Huu Hiep

Dao Huy Cuong

Phan Cao Dat

Thach Phuoc

Mai Thi Hong

Nguyen Ai Nguyen