Two singular problems of dual-phase-lag thermo-porous-elasticity with microtemperatures

Abstract

In a recent paper the authors studied a generic problem determined by the one-dimensional porous-thermoelasticity with microtemperatures in the context of the dual-phase-lag theory. Energy decay rates for that system were obtained. However, there were several cases when the coupling between the different components defining the system of equations is weaker that were not treated. In this paper we are interested in these singular cases and we will prove the polynomial decay of the solutions depending on the relations of the relaxation parameters.