On a mixture of an MGT viscous material and an elastic solid

Abstract A lot of attention has been paid recently to the study mixtures and also Moore–Gibson–Thompson (MGT) type equations or systems. In fact, MGT proposition can be used describe viscoelastic materials. this paper, we analyze a problem involving mixture composed by material an elastic solid. To end, first derive system governing deformations such material. We give suitable assumptions obtain existence uniqueness result. The semigroups theory linear operators is used. paper concludes proving exponential decay solutions with help characterization exponentially stable contractions introducing extra assumption. impossibility location shown.