Decay of waves in strain gradient porous elasticity with Moore-Gibson-Thompson dissipation

We study a one-dimensional problem arising in strain gradient porous-elasticity. Three different Moore–Gibson–Thompson dissipation mechanisms are considered: viscosity and hyperviscosity on the displacements, and weak viscoporosity. The existence and uniqueness of solutions are proved. The energy decay is also shown, being polynomial for the two first situations, unless a particular choice of the constitutive parameters is made in the hyperviscosity case. Finally, for the weak viscoporosity, only the slow decay can be expectedPeer ReviewedPostprint (author's final draft

Decay for strain gradient porous elastic waves

We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t-1/2 . Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more “efficient” than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark-ß scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity casesPeer ReviewedPostprint (published version

Decay for strain gradient porous elastic waves

We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t−1/2. Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more “efficient” than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark-β scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases.Agencia Estatal de Investigación | Ref. PGC2018‐096696‐B‐I00Agencia Estatal de Investigación | Ref. PID2019‐105118GB‐I00Universidade de Vigo/CISU

On the time decay of solutions for non-simple elasticity with voids

In this work we consider the non-simple theory of elastic material with voids and we investigate how the coupling of these two aspects of the material affects the behavior of the solutions. We analyze only two kind of different behavior, slow or exponential decay. We introduce four different dissipation mechanisms in the system and we study, in each case, the effect of this mechanism in the behavior of the solutions.Peer ReviewedPostprint (author's final draft

Decay of quasi-static porous-thermo-elastic waves

We study the behavior in time of the solutions to several systems of equations for porous-thermo-elastic problems when one of the variables is considered to be quasi-static or, in other words, whose second time derivative can be neglected. We analyze three different situations using the classical Fourier law and also the type II or type III Green–Naghdi heat conduction modelsPeer ReviewedPostprint (author's final draft

Exponential decay in one-dimensional porous-thermo-elasticity

This paper concerns the one dimensional problem of the porous-thermo-elasticity. Two kinds of dissipation process are considered: the viscosity type in the porous structure and the thermal dissipation. It is known that when only thermal damping is considered or when only porous damping is considered we have the slow decay of the solutions. Here we prove that when both kinds of dissipation terms are taken into account in the evolution equations the solutions are exponentially stable.Peer Reviewe

Exponential decay in one-dimensional type III thermoelasticity with voids

In this paper we consider the one-dimensional type III thermoelastic theory with voids. We prove that generically we have exponential stability of the solutions. This is a striking fact if one compares it with the behavior in the case of the thermoelastic theory based on the classical Fourier law for which the decayis generically slower.Peer ReviewedPostprint (author's final draft

Energy decay in thermoelastic bodies with radial symmetry

In this paper, we consider the energy decay of some problems involving domains with radial symmetry. Three different settings are studied: a strong porous dissipation and heat conduction, a weak porous dissipation and heat conduction and poro-thermoelasticity with microtemperatures. In all the three problems, the exponential energy decay is shown. Moreover, for each of them some finite element simulations are presented to numerically demonstrate this behaviorPeer ReviewedPostprint (published version