Well-posedness and asymptotic behavior of swelling porous elastic soils with dual-phase-lag thermoelasticity

In this article, we study the second-order dual-phase-lag heat conduction law, incorporating the microstructural interaction effect, in swelling porous elastic soils with fluid saturation. In this theory, two relaxation parameters, τq and τθ, are proposed. We employ the energy method. If 2τθ>τq, we obtain strong thermal dissipation with exponential decay for the total energy of the system. If 2τθ=τq, we get weaker dissipation, and in this case, we prove that the system has polynomial decay.