The asymptotic behavior of solutions of an initial boundary value problem for the generalized Benjamin-Bona-Mahony equation

摘要

The asymptotic behaviors of solutions of an initial-boundary value problem for the generalized BBM equation with non-convex flux are discussed in this paper. It is proved that under the conditions of constant boundary data and small perturbation for the initial data, the global solutions exist and converge time-asymptotically to a stationary wave or the superposition of a stationary wave and a rarefaction wave. The proof is given by a technical L 2-weighted energy method.