Global existence and asymptotic stability for coupled nonlinear Klein–Gordon equations with nonlinear damping terms

Abstract

We study coupled nonlinear Klein–Gordon equations with nonlinear damping and source terms, in a bounded domain with the initial and Dirichlet boundary conditions. The existence of global solutions is discussed by using the potential well method, and the asymptotic stability is also given by applying a lemma due to V. Komornik [Exact controllability and stabilization. The multiplier method. Paris: RAM: Research in Applied Mathematics, Masson-John Wiley; 1994].