Min Chen

Professor of Mathematics, Purdue University

Home ยป Publications

Publications

Research on a two fluid two phase model

  • Analysis of stability, verification and chaos with the Kreiss-Yström model by William D. Fullmer, Martin A. Lopez de Bertodano, Min Chen and Alejandro Clausse, Applied Mathematics and Computation, Vol 248, pp 28-46 (2014)

Research on nonlinear dispersive water waves

  • Singular solutions of a Boussinesq system for water waves, by Jerry Bona and Min Chen, Journal of Mathematical Study, Vol. 49, No. 3, pp. 205-220 (2016)
  • Generalized regularized long waves equations with white noise dispersion, by M. Chen, O. Goubet and Y. Mammeri, Stochastic Partial Differential Equations: Analysis and Computation (2017).
  • Decay of solutions to viscous asymptotical models for waterwaves: Kakutani-Matsuuchi model, with S. Dumont and O. Goubet, Nonlinear Analysis, Vol. 75, pp 2883-2896 (2012).
  • Existence of Traveling-wave Solutions to Boussinesq Systems, with Nghiem V. Nguyen and Shu-Ming Sun, Differential and Integral Equations, Vol. 24, no. 9-10, pp. 895--908 (2011).
  • Spectral stability of stationary solutions of a Boussinesq system describing long waves in dispersive media, with Chris Curtis, Bernard Deconinck, Crystal Lee and Nghiem V. Nguyen, SIAM Journal on Applied Dynamical Systems, Vol 9, No. 3, pp. 999-1018(2010).
  • Oblique Interaction of Solitary waves, Proceeding of the Water Waves: Theory and Experiment, Howard University, USA May 2008, published Apr. 2010.
  • Decay of solutions to a water wave model with a nonlocal viscous dispersive term, with S. Dumont, L. Dupaigne and O. Goubet, Discrete and Continuous Dynamical Systems Series S, Vol 27, No. 4 pp. 1473-1492(2010).
  • Solitary-Wave Solutions to Boussinesq Systems with Large Surface Tension, with Nghiem V. Nguyen and Shu-Ming Sun, Discrete and Continuous Dynamical Systems Series S, vol. 26, no. 4, pp 1153-1184(2009).
  • Long-Time Asymptotics of 2D Dissipative Boussinesq Systems, with O. Goubet, Discrete and Continuous Dynamical Systems Series S, Vol. 2, Number 1, pp 37-53 (2009).
  • From Boussinesq systems to KP-type equations, Canadian Applied Mathematics Quarterly, Vol.15, number 4, Winter 2007.
  • Numerical investigation of a two-dimensional Boussinesq system, Discrete and Continuous Dynamical Systems, Vol. 28, Num. 4, pp.1169-1190. (2009).
  • Asymmetrical Periodic Wave Patterns of two-dimensional Boussinesq systems, with G. Iooss, Physica D, Vol. 237, pp. 1539-1552 (2008).
  • Cnoidal Wave Solutions to Boussinesq Systems, with H. Chen and Nghiem Nguyen, Nonlinearity, Vol. 20, pp. 1443-1461 (2007).
  • Long-Time Asymptotic Behavior of Dissipative Boussinesq System, with O. Goubet, Discrete and Continuous Dynamical Systems, Vol 17, No. 3, pp. 509-528(2007)
  • Periodic Wave Patterns of two-dimensional Boussinesq systems, with G. Iooss, European Journal of Mechanics B/Fluids, vol 25, pp. 393-405 (2006).
  • Comparisons between the BBM equation and a Boussinesq system, with A.A.Alazman, J.P. Albert, J. L. Bona and J. Wu, Advances in Differential Equations, Vol. 11, no. 2, pp. 121-166 (2006).
  • Standing waves for a two-way model system for water waves, with G. Iooss, European Journal of Mechanics B/Fluids, Vol 24, No 1, pp. 113-124 (2005).
  • Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. Part II: the nonlinear theory, with J. L. Bona and J-C. Saut, Nonlinearity, Vol 17, No. 3, pp. 925 - 952.(2004)
  • Equations for bi-directional waves over an uneven bottom, Mathematics and Computers in Simulation, Vol. 62, pp. 3-9 (2003).
  • Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. Part I: derivation and the linear theory, with J. L. Bona and J-C. Saut, Journal of Nonlinear Science, Vol.12, No. 4, pp. 283-318 (2002).
  • Solitary-wave and multi-pulsed traveling-wave solutions of Boussinesq systems, Applicable Analysis, Vol. 75(1-2), pp. 213-240 (2000).
  • A plethora of multi-pulsed solutions for a Boussinesq system, Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp. 274-279, (2000), (refereed);
  • A Boussinesq system for two-way propagation of nonlinear dispersive waves, with J. L. Bona, Physica D. V. 116 1-2, pp. 191-224 (1998).
  • Exact traveling-wave solutions to bi-directional wave equations, International Journal of Theoretical Physics, Vol. 37, No. 5, pp. 1547-1567, (1998).
  • Exact solutions of various Boussinesq systems, Appl. Math. Lett., Vol. 11, No 5, pp. 45-49, (1998)
  • Preliminary results on simulation of a new kind traveling wave of permanent form, Proceedings of the Fourth International Conference on Mathematical and Numerical Aspect of Wave Propagation, pp. 209-213, (1998), (refereed);
  • Higher-order Boussinesq systems for two-way propagations of water waves, with J. Bona, Proceedings of the Conference on Nonlinear Evolution Equations and Infinite-Dimensional Dynamical Systems. (1997)

Research on optical waves

  • Three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities, with D.J. Kaup and Boris A. Malomed, Physical Review E, vol 69, no. 5, 056605 (2004). It is selected for the June 2004 issue of Virtual Journal of Ultrafast Science.

Research on acoustic wave equation

  • Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation, with Monica Torres and Timothy Walsh, Physics Letters A, 373, pp 1037-1043 (2009).

Research on "Incremental Unknown" Method

  • Bifurcations of Finite Difference Schemes and their Approximate Inertial Forms, with R. Bronstering, Mathematical Modeling and Numerical Analysis. Vol. 32, no. 6, pp. 715-728 (1998)
  • The Incremental Unknowns - a multilevel scheme for the simulation of turbulent channel flows, with H. Choi, T. Dubois, J. Shen and R. Temam, Proceedings of the Summer Program 1996, Center for Turbulence Research, Stanford University and NASA Ames Research Center. (1996)
  • Incremental Unknowns in finite differences in three space dimension. with A. Miranville and R. Temam, Comp. Appl. Math., Vol. 14, no. 3, pp. 1-15, (1995).
  • Nonlinear Galerkin method with multilevel Incremental Unknowns, with R. Temam, Contributions in Numerical Mathematics, World Sci. Ser. Appl. Anal., Vol. 2, pp. 151-164, World Sci. Publishing, River Edge, NJ, (1993).
  • Incremental Unknowns in finite differences: condition number of the matrix, with R. Temam, SIAM J. Matrix Analysis and its Appl., Vol. 14, No. 2, (1993).
  • Nonlinear Galerkin method in the finite difference case and Wavelet-like Incremental Unknowns, with R. Temam, Numer. Math., Vol. 64, no. 3, pp. 271-294, (1993).
  • Incremental Unknowns for convection-diffusion equations, with R. Temam, Applied Numerical Mathematics, Vol. 11, pp. 365-383, (1993).
  • Three types of incremental unknowns and nonlinear Galerkin method in the finite difference case, with R. Temam, Advances in computer methods for partial differential equations VII, pp. 109-113, (1992).
  • Incremental Unknowns for solving partial differential equations, with R. Temam, Numer. Math., Vol 59, pp. 255-271, (1991).
  • Incremental Unknown method I, with R. Temam, Appl. Math. Lett., Vol. 4, No. 3, pp. 73-76, (1991).
  • Incremental Unknown method II, with R. Temam, Appl. Math. Lett., Vol. 4, No. 3, pp. 77-80, (1991).

Ph.D and Master's Thesis

  • "Incremental Unknown" methods. Ph.D. Thesis at Indiana University, Bloomington, IN., (1991).
  • A new algorithm for the turbulent spot calculation. Thesis for Master of Science in Engineering. Princeton University, Princeton, NJ., (1988).
  • Reflection of a strong spherical shock wave on a plane wall. Thesis for Master of Science, Beijing University, Beijing, China, (1985).