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

Abstract 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.

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