Abstract:

In this paper,we study the initial-boundary value problem to a generalized Kawahara equation on a bounded interval or a half-line.The energy integral method,the inequality technique and the embedding theorem are used to establish a prior estimate of the solution,and the existence and uniqueness of the global regular solution on a bounded interval are showed by the principle of contraction mapping.It is proved that the L2-norm of the solution has exponential decay when the time tends to infinity. Furthermore,under a stronger condition on the initial boundary values,the existence of a global regular solution on a bounded interval which is independent of the length of the bounded domain,and the existence of a unique global regular solution on a half

-line are derived.

Key words: Generalized Kawahara equation, Global regular solution, Existence, Uniqueness