Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

Abstract

We consider the global existence of strong solutionu, corresponding to a class of fully nonlinear wave equations with strongly damped termsutt-kΔut=f(x,Δu)+g(x,u,Du,D2u)in a bounded and smooth domainΩinRn, wheref(x,Δu)is a given monotone inΔunonlinearity satisfying some dissipativity and growth restrictions andg(x,u,Du,D2u)is in a sense subordinated tof(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solutionu∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).