The influence of damping and source terms on solutions of nonlinear wave equations

Abstract

We discuss in this paper some recent development in the study of nonlinear wave equations. In particular, we focus on those results that deal with wave equations that feature two competing forces.One force is a damping term and the other is a strong source. Our central interest here is to analyze the influence of these forces on the long-time behavior of solutions.

Keywords

• degenerate damping
• generalized solutions
• source terms
• wave equations
• weak solutions
• blow-up of solutions.