Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping

In this paper, we prove the existence, uniqueness, and uniform stability of strong and weak solutions of the nonlinear generalized Klein-Gordon equation (1.1)_1 (see Sec. I) in bounded domains with nonlinear damped boundary conditions given by (1.1)_3 (see Sec. I) with some restrictions on function f(u), h(del u), g(u(t)), and b(x), we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3544046]