Global Existence, Uniqueness, and Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

摘要

This paper is concerned with the global existence, uniqueness, and asymptotic behavior of solution for the nonlinear wave equation with the p-Laplacian operator u_(tt)-div(|▽u|~(p-2)▽u)-△u_t + g(x,u) = f(x), in Ω × (0,∞), (1.1) u(x,0) = u_0(x), u_t(x,0) = u_1(x), in Ω; u(x,t) = 0, on (d)Ω × [0,∞), (1.2) where 2 ≤ p < n and Ω is a boundary domain in R~n with smooth boundary (d)Ω. The assumptions on f, g, u_0 and u_1 will be made in the sequel.