NONLINEAR STABILITY OF PLANAR STATIONARY WAVES FOR GENERALIZED BENJAMIN–BONA–MAHONY–BURGERS EQUATIONS IN THE HALF-PLANE

Abstract

This paper is concerned with the nonlinear stability of planar stationary waves of generalized Benjamin–Bona–Mahony–Burgers equations in half-plane. The planar stationary waves are shown to be globally nonlinear stable and then, by employing the space–time weighted energy method developed by Kawashima and Matsumura in 1995 and a generalized Hardy type inequality with the best possible constant introduced by Kawashima and Kurata in 2009, the corresponding convergence rates (both algebraic and exponential) of the global solutions to the stationary waves are also obtained for both the nondegenerate case and the degenerate case.