NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS

This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar vi...

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Bibliographic Details
Published inActa mathematica scientia Vol. 33; no. 6; pp. 1531 - 1550
Main Author 陈正争 肖清华
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2013
Subjects
35G25
35Q53
Cauchy problem
Conservation laws
Decay
Energy methods
generalized KdV-Burgers equation
L2energy estimate
Mathematical analysis
nonlinear stability
Nonlinearity
Scalars
shock profiles
Stability
平面冲击波
平面激波
广义KdV-Burgers方程
柯西问题
粘性激波
维度
配置文件
非线性稳定性
generalized KdV-Burgers equation
35Q53
nonlinear stability
L2energy estimate
shock profiles
35G25
L2 energy estimate
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ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(13)60102-2

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Summary:This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.
Bibliography:This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.
42-1227/O
generalized KdV-Burgers equation; shock profiles; nonlinear stability; L^2 energy estimate
Zhengzheng CHEN,Qinghua XIAO（1 School of Mathematical Sciences, Anhui University, Hefei 230601, China;2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China）
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(13)60102-2