CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

doi:10.1016/S0252-9602(15)30094-1

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 265-282.doi: 10.1016/S0252-9602(15)30094-1

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

陈正争, 柴晓娟, 王文娟

School of Mathematical Sciences, Anhui University, Hefei 230601, China

收稿日期:2014-09-15 修回日期:2015-05-25 出版日期:2016-01-30 发布日期:2016-01-30
通讯作者: Zhengzheng CHEN,E-mail:chenzzandu@163.com E-mail:chenzzandu@163.com
作者简介:Xiaojuan CHAI,E-mail:chaixj.ahu@gmail.com;Wenjuan WANG,E-mail:wangwenjuan@ahu.edu.cn
基金资助:
This work was supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005) and the Tian Yuan Foundation of China(11426031).

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

Zhengzheng CHEN, Xiaojuan CHAI, Wenjuan WANG

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2014-09-15 Revised:2015-05-25 Online:2016-01-30 Published:2016-01-30
Contact: Zhengzheng CHEN,E-mail:chenzzandu@163.com E-mail:chenzzandu@163.com
Supported by:
This work was supported by the Doctoral Scientific Research Funds of Anhui University(J10113190005) and the Tian Yuan Foundation of China(11426031).

摘要/Abstract

摘要：

This paper is concerned with a singular limit for the one-dimensional compress-ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie(2011) [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie's convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

关键词: radiation hydrodynamics model, singular limit, contact discontinuity, convergence rate, energy estimates

Abstract:

Key words: radiation hydrodynamics model, singular limit, contact discontinuity, convergence rate, energy estimates

中图分类号:

35L65

陈正争, 柴晓娟, 王文娟. CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL[J]. 数学物理学报(英文版), 2016, 36(1): 265-282.

Zhengzheng CHEN, Xiaojuan CHAI, Wenjuan WANG. CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL[J]. Acta mathematica scientia,Series B, 2016, 36(1): 265-282.

参考文献

[1] Lin C J, Coulombel J F, Goudon T. Shock proflies for non-equilibrium radiating gases. Phys D, 2006, 218:83-94
[2] Lin C J, Coulombel J F, Goudon T. Asymptotic stability of shock proflies in radiative hydrodynamics. C R Math Acad Sci Paris, 2007, 345:625-628
[3] Mihalas D, Mihalas B. Foundation of Radiation Hydrodynamics. London:Oxford University Press, 1984
[4] Pomraning G C. The Equations of Radiation Hydrodynamics. New York:Pergamon Press, 1973
[5] Vincenti W, Kruger C. Introduction to Physical Gas Dynamics. New York:Wiley, 1965
[6] Kawashima S, Nishibata S. A singular limit for hyperbolic-parabolic coupled systems in radiation hydro-dynamics. Indiana Univ Math J, 2001, 50:567-589
[7] Hamer K. Nonlinear effects on the propagation of sound waves in a radiating gas. Quart J Mech Appl Math, 1971, 24:155-168
[8] Serre D. Systems of Conservation Laws, Vol 1. Cambridge:Cambridge University Press, 1999
[9] Smoller J. Shock Waves and Reaction-Diffusion Equations. New York:Springer-Verlag, 1994
[10] Atkinson F V, Peletier L A. Similarity solutions of the nonlinear diffusion equation. Arch Rational Meth Anal, 1974, 54:373-392
[11] Duyn C J, Peletier L A. A class of similarity solutions of the nonlinear diffusion equation. Nonlinear Anal, 1976/77, 1(3):223-233
[12] Wang J, Xie F. Singular limit to strong contact discontinuity for a 1D compressible radiation hydrodynamics model. SIAM J Math Anal, 2011, 43:1189-1204
[13] Rohde C, Wang W J, Xie F. Hyperbolic-Hyperbolic relaxation limit for a 1D compreesible radiation hy-drodynamics model:superposition of rarefaction wave and contact wave. Commun Pure Appl Anal, 2013, 12:2145-2171
[14] Wang J, Xie F. Asymptotic stability of viscous contact wave for the 1D radiation hydrodynamics system, J Differ Equ, 2011, 251:1030-1055
[15] Xie F. Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model. Discrete Contin Dyn Syst Ser B, 2012, 17:1075-1100
[16] Rohde C, Xie F. Decay rates to viscous contact wave for a 1D compressible radiation hydrodynamics model. Math Models Methods Appl Sci, 2013, 23:441-469
[17] Ma S X. Zero dissipation limit to strong contact discontinuity for the 1-D compressible Navier-Stokes equations. J Differ Equ, 2010, 48:95-110
[18] Ma S X. Viscous limit to contact discontinuity for the 1-D compressible Navier-Stokes equations. J Math Anal Appl, 2012, 387:1033-1043
[19] Kawashima S, Nikkuni Y, Nishibata S. Larger-time behavior of solutions to hyperbolic-elliptic coupled systems. Arch Ration Mech Anal, 2003, 170:297-329
[20] Kawashima S, Nikkuni Y, Nishibata S. The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics//Analysis of Systems of Conservation Laws. Chapman and Hall/CRC, 1997:87-127
[21] Kawashima S, Nishibata S. Weak solutions with a shock to a model system of the radiating gas. Sci Bull Josai Univ, 1998, 5:119-130
[22] Kawashima S, Nishibata S. Cauchy problem for a model system of the radiating gas:weak solutions with a jump and classical solutions. Math Models Methods Appl Sci, 1999, 9:69-91
[23] Kawashima S, Nishibata S. Shock waves for a model system of a radiating gas. SIAM J Math Anal, 1999, 30:95-117
[24] Lattanzio C, Marcati P. Golobal well-posedness and relaxation limits of a model for radiating gas. J Differ Equ, 2003, 190:439-465
[25] Lattanzio C, Mascia C, Serre D. Shock waves for radiative hyperbolic-elliptic systems. Indiana Univ Math J, 2007, 56:2601-2640
[26] Huang F M, Li M J, Wang Y. Zero dissipation limit to rarefaction wave with vacuum for the 1-D com-pressible Navier-Stokes equations. SIAM J Math Anal, 2012, 44:1742-1759
[27] Huang F M, Li X. Zero dissipation limit to rarefaction waves for the 1-D compressible Navier-Stokes equations. Chin Ann Math Ser B, 2012, 33:385-394
[28] Gao W L, Zhu C J. Asymptotic decay toward the planar rarefaction waves for a model system of the radiating gas in two dimensions. Math Models Methods Appl Sci, 2008, 18:511-541
[29] Gao W L, Ruan L Z, Zhu C J. Decay rates to the planar rarefaction waves for a model system of the radiating gas in n dimensions. J Differ Equ, 2008, 244:2614-2640
[30] Lin C J. Asymptotic stability of rarefaction waves in radiative hydrodynamics. Commun Math Sci, 2011, 9:207-223
[31] Xiao Q H, Liu Y N, Kim J S. Asymptotic behavior of rarefaction waves for a model system of a radiating gas. J Inequal Appl, 2012, Art ID:81
[32] Nguyen T, Plaza R G, Zumbrun K. Stability of radiative shock profiles for hyperbolic-elliptic coupled systems. Phys D, 2010, 239:428-453
[33] Francesco M Di. Initial value problem and relaxation limits of the Hamer model for radiating gases in several space variables. NoDEA Nonlinear Differential Equations Appl, 2007, 13:531-562
[34] Hong H, Huang F M. Asymptotic behavior of solutions toward the superposition of contout discontinuity and shock wave for compressible Navier-Stokes equations with free boundary. Acta Math Sci, 2012, 32B(1):389-412
[35] Xin Z P. Zero dissipation limit to rarefaction waves for the one-dimensional Navier-Stokes equations of compressible isentropic gases. Comm Pure Appl Math, 1993, 46:621-665

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

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