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

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. Turn MathJax on Second we consider the case h(∇u)=−∇ϕ⋅∇uh(∇u)=−∇ϕ⋅∇u. In both first and second cases, we have the nonlinear boundary condition View the MathML source∂u∂ν+∫0tk(t−s,x)u′(s)ds+a(x)g(u′)=0. Turn MathJax on We study energy decay using the multiplier technique and equivalent energy.