GLOBAL EXISTENCE AND DECAY OF ENERGY FOR A NONLINEAR WAVE EQUATION WITH p-LAPLACIAN DAMPING

摘要

This paper presents a study of the nonlinear wave equation with ρ-Laplacian damping: u_(tt) - Δu - Δ_p~u_t = f(u) evolving in a bounded domain Ω C R~n with Dirichlet boundary conditions. The nonlinearity f(u) represents a strong source which is allowed to have a supercritical exponent, i.e., the Nemytski operator f(u) is not locally Lipschitz from H_0~1(Ω) into L~2(Ω). The nonlinear term - Δ_p~u_t acts as a strong damping where the - Δ_p denotes the ρ-Laplacian. Under suitable assumptions on the parameters and with careful analysis involving the Nehari Manifold, we prove the existence of a global solution and estimate the decay rates of the energy.