Asymptotic behavior in nonlocal Mindlin's strain gradient thermoelasticity with voids and microtemperatures

A nonlocal theory for thermoelastic materials with voids and microtemperatures based on Mindlin's strain gradient theory was derived in this paper. The obtained system of equations is a coupling of a two second-order in time equations with higher gradients terms due to the strain gradient length scale parameter / and the elastic nonlocal parameter (sic) coupled with two parabolic equations. This poses some new mathematical difficulties due to the lack of regularity. Using the semigroup theory, we show the well-posedness of the one dimensional problem. By an approach based on the Gearhart-Herbst-Pruss-Huang theorem, we prove that the associated semigroup is exponentially stable; but not analytic. (C) 2022 Elsevier Inc. All rights reserved.