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.

本研究研究了具有双孔隙结构的热弹性材料的混合初始边值问题，并考虑了微温度的影响。通过将问题转化为柯西型问题来确定解的存在性。考虑到方程、未知数和条件的复杂性，我们在特定的希尔伯特空间内应用收缩半群理论。我们使用 Lax-Milgram 定理证明了解的存在性。此外，该解决方案的独特性是基于 Lumer-Phillips 推论证明的，该推论对应于 Hille-Yosida 定理。在最后一节中，我们展示了解对微温度双多孔热弹性混合初始边值问题的连续依赖性。