Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach

The stability features of the dissipative porous elastic systems have piqued the interest of several researchers. The desired exponential decay property of the energy is obtained unless the nonphysical equal speed condition is imposed. This work analyzes the porous elastic system with micro-temperature. First, the exponential stability is obtained in case where there is an assumption on physical constants. Then from a second-spectrum viewpoint, the system’s global well-posedness is proved using the Faedo–Galerkin method. Later, we prove that the microtemperature effect is enough to get the exponential stability of the solution without any assumption on the physical constants. A numerical scheme is introduced. Finally, we present some numerical results which demonstrates the exponential behavior of the solution.