GLOBAL EXISTENCE TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR DIFFUSION AND WAVE EQUATIONS II

Abstract

We prove the global existence and uniqueness of the strong solution pair (u, v) to the initial-boundary value problem for coupled equations of an m-Laplacian-type diffusion equation and a nonlinear wave equation. The interaction of the two equations is given through nonlinear source terms f (u, v) and g(u, v). To derive the required a priori estimates we employ a ‘loan' method. The estimation of the L^∞-norm of solutions of the nonlinear parabolic equation due to Moser's iteration method is a key step of our argument.