Global existence and uniform decay for wave equation with dissipative term and boundary damping

In this paper,we prove the existence, uniqueness and uniform stability of strong and weak solutions of the nonlinear wave equation utt 􀀀 1u C b.x/ut C f .u/ D 0 in bounded domains with nonlinear damped boundary conditions, given by @u @ C g.ut / D 0; with restrictions on function f .u/; g.ut / and b.x/;. We prove the existence by means of the Glerkin method and obtain the asymptotic behavior by using of the multiplier technique from the idea of Kmornik and Zuazua (see [7]).