Stability of thermoelastic diffusion problem of type III in spaces of different dimensions

Abstract

AbstractIn this article, we study the stability issues of a thermoelastic diffusion problem of type III in spaces of different dimensions. First we prove that the one‐dimensional problem is exponentially stable without adding damping terms. Then we prove the lack of exponential stability in the two‐dimensional space. Moreover, a frictional damping for the elastic component leads to the exponential stability in three‐dimensional space. As the form of the damping term depends on the nature of the material, we will distinguish the case of isotropic materials and the case of anisotropic materials.