Study Of Non-homogeneous MGT Equations With Memory

Considering the inhomogeneous Moore-Gibson-Thompson equation with memory?uttt+?utt+c2Au+bAut-?0tg(t-s)Au(s)ds=|u|pu,In this paper, we are interested in the energy decay of the inhomogeneous Moore-Gibson-Thompson equation with memory in Hilbert space. On the assumption of the initial value and the memory kernel function, we show that the decay rate of the energy function depends on the decay properties of the memory kernel function.There are three steps in the proof process of the paper:First step, we develops a method to construct energy functional E(t). According to the formula d/dtE(t) =-R(t), we can get preliminary estimates of the energy functions through the estimate of R(t);Second step, constructing the equivalent functional H(t) of energy functional E(t);Third step, using differential method and integral method to estiate the energy func-tion E(t), we can obtain the exponential decay of the energy function E(t) when the memory kernel decays exponentially.