On porous-elastic systems with Fourier law

Exponential decay in one-dimensional type III thermoelasticity with voids

“…There, the author showed that generically the porous dissipation is not strong enough to guarantee the exponential decay of the solutions for a porous elastic structure. From this contribution a big quantity of contributions have been developed to clarify the decay of the thermomechanical perturbations for elastic solids with voids when dierent eects are taken into account [1,3,10,11,18,21,27,29,30,33]. It is accepted that generically we would need two dissipative mechanisms to guarantee the exponential decay of solutions.…”

“…It was possible to obtain the exponential stability when some other dissipative mechanisms were also present as well as the microtemperatures [2] or the porous dissipation [3]. In fact Muñoz-Rivera and Quintanilla [27] proved the polynomial decay under suitable conditions on the coecients and very recently new results for this problem have been obtained [33]. That is, in general the thermal eects (based on the classical Fourier law) are not strong enough to bring all the system to the exponential stability.…”

Stabilization for an inhomogeneous porous‐elastic system with temperature and microtemperature

“…However, Santos et al. [40], proved that the system is exponentially stable if and only if equal‐speed wave propagations. Leseduarte et al.…”

Global and exponential attractors for a nonlinear porous elastic system with delay term

“…In recent years, a large number of studies have been performed related to the asymptotic behavior of solutions of elastic pore models subject to the most diverse damping mechanisms (cf. [5,10,21,29,36,37,44,48,49,50]).…”