We study a system of nonlinear Klein-Gordon equations with viscoelastic and degenerate damping in bounded domain. prove the global existence exponential growth solutions negative initial energy.

In this paper, we are interested in the global existence result for a class of Klein–Gordon equations, particularly unified time decay concerning possibly vanishing mass parameter. We give first rigorous proof problem, which relies on both flat foliation and hyperboloidal Minkowski spacetime. To take advantage foliations, an iteration procedure is used.