Energy decay for nondissipative distributed systems with boundary damping and source term

In this paper we consider energy decay for nondissipative distributed systems with boundary damping and source terms. First we consider the wave equation u″−Δu+h(∇u)=|u|ρu.u″−Δu+h(∇u)=|u|ρu. Second we consider the case h(∇u)=−∇ϕ⋅∇uh(∇u)=−∇ϕ⋅∇u. In both first and second cases, we have the nonlinear boundary condition ∂u∂ν+∫0tk(t−s,x)u′(s)ds+a(x)g(u′)=0. We study energy decay using the multiplier technique and equivalent energy.