Well‐posedness and exponential decay for the Moore–Gibson–Thompson equation with time‐dependent memory kernel

Abstract

We are interested in the well-posedness and exponential decay of Moore-Gibson-Thompson equation with memoryHere, the main feature is that the memory kernel h t (•) depends on time. By using the linear semigroup theory, we prove that the above system is global well-posedness. In addition, the exponential decay of the related energy is shown to occur, provided that the memory kernel is controlled by a negative exponential.

A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids

“…In this work, we want to focus on the theory of heat conduction called Moore-Gibson-Thompson. It is worth recalling that this theory has received much attention in the last four years [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] since many authors have investigated the qualitative and quantitative properties of the solutions to this equation. If we consider the type III heat conduction theory proposed by Green-Naghdi [6], we can see that it is based on the constitutive equation in the case of centrosymmetric materials:…”

“…In this work, we want to focus on the theory of heat conduction called Moore‐Gibson‐Thompson. It is worth recalling that this theory has received much attention in the last four years [10–24] since many authors have investigated the qualitative and quantitative properties of the solutions to this equation. If we consider the type III heat conduction theory proposed by Green‐Naghdi [6], we can see that it is based on the constitutive equation in the case of centrosymmetric materials: $$$$\begin{equation*} q_i=k_{ij} \alpha _{,j}+ \kappa _{ij}^* \theta _{,j}, \end{equation*}$$$$where $$q_i$$ is the heat flux vector, θ is the temperature and α is the thermal displacement.…”