On time periodic solutions to the generalized BBM-burgers equation with time-dependent periodic external force

Abstract

In this paper, we consider the generalized BBM-Burgers equation with periodic external force in Rn. Existence and uniqueness of time periodic solutions that have the same period as the external force are established in some suitable function space for the space dimension n≥ 3. Moreover, we also discuss the time asymptotic stability of the time periodic solution. The proof is mainly based on the contraction mapping theorem and continuous argument.

Keywords

• generalized BBM-Burgers equation
• existence of time periodic solutions
• asymptotic stability