Asymptotic stability of a composite wave of two viscous shock waves for the one-dimensional radiative Euler equations

被引：24

作者：

Fan, Lili ^{[1
]}

Ruan, Lizhi ^{[2
]}

Xiang, Wei ^{[3
]}

机构：

[1] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Hubei, Peoples R China

[2] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China

[3] City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2019年 / 36卷 / 01期

关键词：

Radiative Euler equations; Viscous shock waves; Diffusion wave; Stability; PLANAR RAREFACTION WAVES; L-INFINITY-STABILITY; MODEL SYSTEM; TRAVELING-WAVES; CONTACT DISCONTINUITY; NONLINEAR STABILITY; CONVERGENCE-RATES; GAS; PROFILES; DECAY;

D O I：

10.1016/j.anihpc.2018.03.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of the wellposedness of the radiative Euler equations. By employing the anti-derivative method, we show the unique global-in-time existence and the asymptotic stability of the solutions of the radiative Euler equations for the composite wave of two viscous shock waves with small strength. This method developed here is also helpful to other related problems with similar analytical difficulties. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：1 / 25

页数：25

共 53 条

[1] Asymptotic analysis of fluid models for the coupling of radiation and hydrodynamics [J].

Buet, C ;

Despres, B .

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 2004, 85 (3-4) :385-418

[2] Analysis of large amplitude shock profiles for non-equilibrium radiative hydrodynamics: formation of Zeldovich spikes [J].

Coulombel, J. -F. ;

Goudon, T. ;

Lafitte, P. ;

Lin, C. .

SHOCK WAVES, 2012, 22 (03) :181-197

[3] Initial value problem and relaxation limits of the hamer model for radiating gases in several space variables [J].

Di Francesco, Marco .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 13 (5-6) :531-562

[4] Energy method for multi-dimensional balance laws with non-local dissipation [J].

Duan, Renjun ;

Fellner, Klemens ;

Zhu, Changjiang .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2010, 93 (06) :572-598

[5]

Duan RJ, 2012, MATH MOD METH APPL S, V22, P39

[6] Asymptotic stability of a composite wave of two viscous shock waves for a one-dimensional system of non-viscous and heat-conductive ideal gas [J].

Fan, Lili ;

Matsumura, Akitaka .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (04) :1129-1157

[7] Decay rates to the planar rarefaction waves for a model system of the radiating gas in n dimensions [J].

Gao, Wenliang ;

Ruan, Lizhi ;

Zhu, Changjiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (10) :2614-2640

[8] Asymptotic decay toward the planar rarefaction waves for a model system of the radiating gas in two dimensions [J].

Gao, Wenliang ;

Zhu, Changjiang .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (04) :511-541

[9] Coupled model for radiative transfer: Doppler effects, equilibrium, and nonequilibrium diffusion asymptotics [J].

Godillon-Lafitte, P ;

Goudon, T .

MULTISCALE MODELING & SIMULATION, 2005, 4 (04) :1245-1279

[10] NON-LINEAR EFFECTS ON PROPAGATION OF SOUND WAVES IN A RADIATING GAS [J].

HAMER, K .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1971, 24 (MAY) :155-&

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