Attenuation of an external signal in a thermoelastic material with triple porosity in local thermal non-equilibrium

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.

Keywords:

• Depth of an external signal
• local thermal non-equilibrium
• spatial behavior
• transmission depth of an external thermo-mechanical perturbation
• triple porosity

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 74F05
• 74F10
• 74L05
• 74M25

Acknowledgment

The author acknowledges support from the Project STARDUST-R H2020-MSCA-ITN-2018, Grant Agreement number 813644, Alexandru Ioan Cuza University of Iasi.

Disclosure statement

The author has no conflict of interests to declare.