-coupling mechanisms are sufficient to obtain exponential decay in strain gradient elasticity

Abstract In this paper, we consider the time decay of solutions to some problems arising in strain gradient thermoelasticity. We restrict two-dimensional case, and assume that two dissipative mechanisms are introduced, temperature mass dissipation. First, show problem is well-posed proving operator defining it generates a contractive semigroup linear operators. Then, assuming function involving coupling terms elliptic, exponential concluded as well analyticity solutions. Finally, describe how obtain stability case hyperbolic