Selected publications of Min
Chen
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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).
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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).
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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).
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Oblique Interaction of Solitary waves,
Proceeding of the Water Waves: Theory and Experiment, Howard University, USA
May 2008, published Apr. 2010.
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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).
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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).
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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).
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From Boussinesq systems to KP-type equations, Canadian Applied Mathematics
Quarterly, Vol.15, number 4, Winter 2007.
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Numerical investigation of
a two-dimensional Boussinesq system,
Discrete and Continuous Dynamical Systems, Vol. 28, Num. 4, pp.1169-1190. (2009).
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Asymmetrical Periodic Wave Patterns of two-dimensional Boussinesq systems, with G. Iooss,
Physica D, Vol. 237, pp. 1539-1552 (2008).
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Cnoidal Wave Solutions to Boussinesq Systems,
with H. Chen and Nghiem Nguyen, Nonlinearity, Vol. 20, pp. 1443-1461
(2007).
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Long-Time Asymptotic Behavior of Dissipative
Boussinesq System, with O. Goubet,
Discrete and Continuous Dynamical Systems, Vol 17, No. 3, pp. 509-528(2007)
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Periodic Wave Patterns of two-dimensional Boussinesq systems, with G. Iooss,
European Journal of Mechanics B/Fluids, vol 25, pp. 393-405 (2006).
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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).
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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).
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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)
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Equations for bi-directional waves over an uneven bottom,
Mathematics and Computers in Simulation, Vol. 62, pp. 3-9 (2003).
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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).
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Solitary-wave and multi-pulsed
traveling-wave solutions of Boussinesq systems, Applicable Analysis,
Vol. 75(1-2), pp. 213-240 (2000).
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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);
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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).
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Exact traveling-wave solutions to
bi-directional wave equations, International Journal of Theoretical
Physics, Vol. 37, No. 5, pp. 1547-1567, (1998).
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Exact solutions of various Boussinesq systems,
Appl. Math. Lett., Vol. 11, No 5, pp. 45-49, (1998)
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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)
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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.
-
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).
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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)
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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)
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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).
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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).
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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).
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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).
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Incremental Unknowns for convection-diffusion equations,
with R. Temam, Applied Numerical Mathematics, Vol. 11, pp. 365-383, (1993).
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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).
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Incremental Unknowns for solving partial differential
equations, with R. Temam, Numer. Math., Vol 59, pp. 255-271, (1991).
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Incremental Unknown method I, with R. Temam, Appl. Math.
Lett., Vol. 4, No. 3, pp. 73-76, (1991).
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Incremental Unknown method II, with R. Temam, Appl. Math.
Lett., Vol. 4, No. 3, pp. 77-80, (1991).
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"Incremental Unknown" methods. Ph.D. Thesis at Indiana
University, Bloomington, IN., (1991).
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A new algorithm for the turbulent spot calculation. Thesis
for Master of Science in Engineering. Princeton University, Princeton,
NJ., (1988).
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Reflection of a strong spherical shock wave on a plane
wall. Thesis for Master of Science, Beijing University, Beijing, China,
(1985).
Abstract