WELL-POSEDNESS FOR A LINEAR BENJAMIN-BONA-MAHONY-BURGERS EQUATION WITH PERIODIC BOUNDARY CONDITIONS

Abstract

This article is concerned with the study of the solutions of a linear Benjamin-Bona-Mahony-Burgers (BBMB) equation. We show that the initial value problem is well-posed in periodic Sobolev spaces s (0, 2 ) s (0, 2 ) s (0, 2 ) p p p H π ×, foHr all s ∈π R,× inH the senπse that we establish global existence and uniqueness theorems for this equation.