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(∇u), g(ut), 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.