Mathematical modelling in nonlocal Mindlin’s strain gradient thermoelasticity with voids

A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient was derived in this paper some qualitative properties. We have also established the size effect of heat conduction aids extended irreversible thermodynamics and generalized free energy. The obtained system equations is a coupling three higher gradients terms due to length scale parameters ϖ l . This poses new mathematical difficulties lack regularity. Based nonlinear semigroups monotone operators, we establish existence uniqueness weak strong solutions one dimensional problem. By an approach Gearhart-Herbst-Prüss-Huang theorem, prove that associated semigroup exponentially stable; but not analytic.