Abstract

This work aims to highlight, by a series of spatial estimates, the effect of the presence of pore system and local thermal non-equilibrium properties in a triple porosity material matrix on the transmission depth of a thermo-mechanical signal. Two kind of spatial behaviors are established, for which the spatial response obeys a linear first-order differential inequality with two kind different coefficients: one is time independent and the other is time dependent. The first differential inequality furnishes some exponential decaying spatial estimates with uniform in time exponent and such estimates are recommended to be used for appropriately large values of the time variable. While the second first-order differential inequality furnishes some exponential decaying spatial estimates with time dependent exponent, thus showing a rapid spatial decrease of the solution for appropriate short values of time. These results are compared with their counterparts without mechanical effects, that is for purely pore system or local thermal non-equilibrium effects theories: this is done for appropriate short and large values of the time variable.

摘要

这项工作旨在通过一系列空间估算来突出三孔材料矩阵中孔隙系统的存在和局部热非平衡特性对热机械信号传输深度的影响。建立了两种空间行为，它们的空间响应服从线性一阶微分不等式，具有两种不同的系数：一种与时间无关，另一种与时间有关。一阶微分不等式提供了一些指数衰减的空间估计，并且时间指数一致，因此建议将这种估计用于较大的时间变量值。尽管第二阶一阶微分不等式提供了一些随时间变化的指数衰减空间估计，因此，在适当的短时间范围内，解决方案的空间快速减小。将这些结果与没有机械作用的结果进行比较，这是针对纯孔隙系统或局部热非平衡作用理论的结果：对于适当的短时变量值和大时变量值可以进行此操作。