A qualitative analysis on the double porous thermoelastic bodies with microtemperature

This study examines a mixed initial-boundary value problem in thermoelastic materials with a double porosity structure, taking into account the effects of microtemperature. The existence of a solution is established by converting the problem into a Cauchy-type problem. Given the complexity of the equations, unknowns, and conditions, we apply contraction semigroup theory within a specific Hilbert space. We prove the existence of a solution using the Lax-Milgram theorem. Additionally, the uniqueness of the solution is demonstrated based on the Lumer-Phillips corollary, which corresponds to the Hille-Yosida theorem. In the final section, we show the continuous dependence of the solution on the mixed initial-boundary value problem for double porous thermoelasticity with microtemperature.