Nonlinear boundary stabilization of the wave equations with variable coefficients and time dependent delay

摘要

We study the stabilization the wave equations with variable coefficients in a bounded domain and nonlinear boundary feedback with time dependent delay. By the Riemannian geometry methods and a suitable assumption of delay, we obtain the exponential decay when the nonlinear terms are linearly bounded and a general decay when the nonlinear terms have no upper growth bound.