Existence of Global Decaying Solutions to the Cauchy Problem for a Nonlinear Dissipative Wave Equation of Klein-Gordon Type with a Derivative Nonlinearity

Abstract

We prove the existence of global decaying solutions to the Cauchy problem for the wave equation of Klein-Gordon type with a nonlinear dissipation and a derivative nonlinearity. To derive required estimates of solutions we employ a delicate 'loan' method.