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

doi:10.1016/S0252-9602(13)60102-2

Abstract

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

CLC Number:

35Q53

CHEN Zheng-Zheng, XIAO Qing-Hua. NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS[J].Acta mathematica scientia,Series B, 2013, 33(6): 1531-1550.

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