Degenerate boundary layer solutions to the generalized benjamin-bonamahony-burgers equation

This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation to the corresponding degenerate boundary layer solutions in the half-space. It is shown that the convergence rate is as t → 1 provided that the initial perturbation lies in for , where q is the degeneracy exponent of the flux function. Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1].