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

Abstract

We are interested in the Moore-Gibson-Thompson(MGT) equation with memory \begin{equation}\nonumber τu_{ttt}+ αu_{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.

24 pages

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