Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy

TL;DR

This paper investigates the Moore-Gibson-Thompson equation with memory effects, analyzing how different types of memory influence energy decay and damping mechanisms in the system.

Contribution

It classifies memory types in the MGT equation and studies their roles in energy decay and damping mechanisms.

Findings

Memory induces damping depending on its type.

Exponential decay of energy is achieved under certain memory conditions.

Memory effects significantly influence the stability of the system.

Abstract

We are interested in the Moore-Gibson-Thompson(MGT) equation with memory \begin{equation}\nonumber \tau u_{ttt}+ \alpha u_{tt}+c^2\A u+b\A u_t -\int_0^tg(t-s)\A w(s)ds=0. \end{equation} We first classify the memory into three types. Then we study how a memory term creates damping mechanism and how the memory causes energy decay.