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Lord–Shulman Thermoelasticity with Microtemperatures
Applied Mathematics and Optimization ( IF 1.8 ) Pub Date : 2020-06-06 , DOI: 10.1007/s00245-020-09691-2
Noelia Bazarra , José R. Fernández , Ramón Quintanilla

In this paper we consider the Lord–Shulman thermoelastic theory with porosity and microtemperatures. The new aspect we propose here is to introduce a relaxation parameter in the microtemperatures. Then we obtain an existence theorem for the solutions. In the case that a certain symmetry is satisfied by the constitutive tensors, we prove that the semigroup is dissipative. In fact, an exponential decay of solutions can be shown for the one-dimensional case. In the last section, we restrict our attention to the case where we have an isotropic and homogeneous material without porosity effects and assuming that two of the constitutive parameters have the same sign. We see that the semigroup is dissipative.



中文翻译:

洛德·舒尔曼微温热弹性

在本文中,我们考虑了具有孔隙度和微观温度的Lord-Shulman热弹性理论。我们在此提出的新方面是在微观温度中引入松弛参数。然后我们获得了解的存在性定理。在本构张量满足一定对称性的情况下,我们证明了半群是耗散的。实际上,对于一维情况,可以显示解的指数衰减。在最后一部分中,我们将注意力集中在具有各向同性且均质的材料而没有孔隙率影响的情况下,并假设两个本构参数具有相同的符号。我们看到半群是耗散的。

更新日期:2020-06-06
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