Global existence, asymptotic behavior and blow-up of solutions for coupled Klein-Gordon equations with damping terms

This paper studies the Cauchy problem for the coupled system of nonlinear Klein-Gordon equations with damping terms. We first state the existence of standing wave with ground state, based on which we prove a sharp criteria for global existence and blow-up of solutions when E(0) < d. We then introduce a family of potential wells and discuss the invariant sets and vacuum isolating behavior of solutions for 0 < E(0) < d and E(0) <= 0, respectively. Furthermore, we prove the global existence and asymptotic behavior of solutions for the case of potential well family with 0 < E(0) < d. Finally, a blow-up result for solutions with arbitrarily positive initial energy is obtained. (C) 2010 Elsevier Ltd. All rights reserved.