Nonlinear stability of generalized Benjamin-Bona-Mahony-Burgers shock profiles in several dimensions

This paper is concerned with nonlinear stability of planar viscous shock profiles of the generalized Benjamin-Bona-Mahony-Burgers equations in two dimensions. Our analysis is motivated by J. Goodman's work (1989) [4] on the nonlinear stability of scalar viscous shock profiles in two dimensions and is based on some new decay estimates on the planar viscous shock profiles of the generalized Benjamin-Bona-Mahony-Burgers equations.