NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS - 陈正争 肖清华 (Acta mathematica scientia, 2013)
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.