On the stability in phase-lag heat conduction with two temperatures

We investigate the well-posedness and the stability of the solutions for several Taylor approximations of the phase-lag two-temperature equations.We give conditions on the parameters which guarantee the existence and uniqueness of solutions as well as the stability and the instability of the solutions for each approximationPeer ReviewedPostprint (author's final draft

On the exponential decay of solutions in dual-phase-lag porous thermoelasticity

In the last years, a big interest has been developed to understand the time decay of solutions for the porous thermoelasticity with different thermal mechanisms. We here want to consider the problem of the one-dimensional porous thermoelasticity when the heat conduction is given by means of the dual-phase-lag theory. We want to give suitable conditions in order to guarantee that the decay of solutions is controlled by a negative exponential. We also want to provide conditions for the slow decay of the solutions.Peer ReviewedPostprint (published version