Uniform decay in a wave equation and Numerical simulations

Abstract

This research paper focuses on investigating the phenomenon of uniform decay in a wave equation. The study encompasses scenarios involving dynamic boundary conditions, localized memory terms, and fractional dampings. The main objective is to establish that the presence of a localized memory term, in conjunction with frictional dampings, holds significant strength. This combined effect, operating through a transmission process (u on the boundary Γ equals v), is demonstrated to ensure the asymptotic stability of the entire system.