EXISTENCE OF GLOBAL DECAYING SOLUTIONS TO THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASILINEAR VISCOELASTIC EQUATIONS OF p-LAPLACIAN TYPE WITH A DERIVATIVE NONLINEARITY

Abstract

We prove the existence of global decaying solutions to the initial boundary value problem for the quasilinear wave equation of p-Laplacian type with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and a difference inequality for the energy.