Energy decay rate of a transmission system governed by degenerate wave equation with drift and under heat conduction with memory effect

TL;DR

This paper studies the energy decay rates of a transmission system combining a degenerate wave equation with heat conduction laws that include memory effects, establishing polynomial and exponential stability results.

Contribution

It introduces a novel analysis of stabilization for a transmission system with degenerate wave and heat equations under memory-effect heat conduction laws, providing decay rate estimates.

Findings

Polynomial decay rate of t^{-4} under Coleman-Gurtin law

Exponential stability under Gurtin-Pipkin law

New insights into energy decay in systems with memory effects

Abstract

In this paper, we investigate the stabilization of transmission problem of degenerate wave equation and heat equation under Coleman-Gurtin heat conduction law or Gurtin-Pipkin law with memory effect. We investigate the polynomial stability of this system when employing the Coleman-Gurtin heat conduction, establishing a decay rate of type $t^{-4}$. Next, we demonstrate exponential stability in the case when Gurtin-Pipkin heat conduction is applied.