Stabilization of a Semilinear Wave Equation With Time-Dependent Variable Coefficients and a Time Varying Delay on the Viscoelastic Boundary

Abstract

This paper focuses on the stabilization of a semilinear wave equation with time-dependent variable coefficients and nonlinear delay on the memory-type boundary, subject to nonlinear boundary dissipation. The existence of weak solution is obtained by means of Faedo-Galerkin approximation and denseness argument. We employ the Riemannian geometry method and convex properties to establish the asymptotic decay rates for the energy. This is achieved through an intrinsic algorithm driven by solutions of an ODE. Moreover, we explore two simple models that aim to contribute to the understanding of how the boundary memory works. Additionally, we give an example of the vector field used to construct geometric multipliers under semilinear conditions.