On the existence of global solutions for a nonlinear Klein-Gordon equation

Abstract

The aim of this work is to study the global existence of solutions for the Cauchy problem of a Klein-Gordon equation with high energy initial data. The proof relies on constructing a new functional, which includes both the initial displacement and the initial velocity: with sign preserving property of the new functional we show the existence of global weak solutions.

Continuous dependence of solutions to the strongly damped nonlinear Klein{Gordon equation

“…By this, the exponential decay rate of the global solutions was proved. Polat and Taskesen [16] also investigated the existence of solutions globally for equation (1), where α = 0, β = 1 by using the potential well method. Moreover, asymptotic behavior of global solutions was obtained by Xu [19].…”