数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (6): 1531-1550.doi: 10.1016/S0252-9602(13)60102-2

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

陈正争*|肖清华   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2012-08-12 出版日期:2013-11-20 发布日期:2013-11-20

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

 CHEN Zheng-Zheng*, XIAO Qing-Hua   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2012-08-12 Online:2013-11-20 Published:2013-11-20

摘要:

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.

关键词: generalized KdV-Burgers equation, shock profiles, nonlinear stability, L2 energy estimate

Abstract:

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.

Key words: generalized KdV-Burgers equation, shock profiles, nonlinear stability, L2 energy estimate

中图分类号: 

  • 35Q53