Stabilization of wave equations with variable coefficients and internal memory

Abstract

In this article, we consider the stabilization of a wave equation with variable coefficients and internal memory in an open bounded domain, by the Riemannian geometry approach. For the wave equation with a locally distributed memory with a kernel, we obtain exponential decay of the energy under some geometric conditions. In addition, for the wave equation with nonlinear internal time-varying delay without upper bound, we obtain uniform decay of the energy.

Keywords

• Stabilization
• wave equation with variable coefficients
• memory term
• time-varying delay
• geometric conditions