Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients

In this article, we study the hyperbolic problem K( x;t) utt ∑n=1 ( a( x;t) uxj ) + F ( x;t;u; ∇u) = 0 u = 0 on 1; @u + ( x) ut = 0 on 0 u(0) = u 0 ; ut(0) = u 1 in Ω ; where Ω is a bounded region in R n whose boundary is partitioned into two disjoint sets 0; 1. We prove existence, uniqueness, and uniform stabil- ity of strong and weak solutions when the coefficients and the boundary conditions provide a damping effect.