Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

Abstract

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