Decay of solutions for a one-dimensional porous elasticity system with memory: the case of non-equal wave speeds

Abstract

In previous work, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations. In this paper, we extend the result to the case of non-equal wave speeds, which is more realistic from the physics point of view.

Asymptotic stability for a laminated beam with structural damping and infinite memory

“…piecewise constant) memory kernel. For more papers related to the Timoshenko beam with memory, we refer the reader to the works of Ammar-Khodja et al [21], Feng and Yin [22], Guesmia and colleagues [23][24][25], Muñoz Rivera and Fernández Sare [26] and references therein. It is worth mentioning that there is no result concerning a laminated beam with structural damping and infinite memory.…”

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.…”

On the decay rates for a one-dimensional porous elasticity system with past history

“…By assuming g (t) ≤ −η(t)g(t), the author established a general decay result in the case of the equal-speed wave propagation case under the assumption that the constant b is positive. Recently, the present author and his co-author, Feng and Yin [11], extended the result to the case of the non-equal wave speeds, and the result also holds for b < 0. For more results concerning the stability to porous elastic solids, one can refer to [12,23,26,29,30,31] and so on.…”