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

Abstract

Abstract: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.

Analysis for the strain gradient theory of porous thermoelasticity

“…where ǫ 2 is a small positive constant and C 4 is a computable positive constant. In view of (21) and (24) we get that…”

“…In the present work, we consider the theory of thermoelasticity when porous and strain gradient effects are combined. It is worth noting that, recently, another contribution concerning time decay estimates has been presented for the joint combination of these two effects but in the isothermal case [24]. Here, we restrict our attention to the one-dimensional theory and we study several qualitative aspects about the behavior of the solutions.…”

Time decay for porosity problems

“…That is, materials with an elastic matrix where we can find voids of the material. This kind of materials with different damping mechanisms has received a huge attention in the last years (see, e.g., 4–22 ). A good survey of this theory can be found in the book of Ieşan 23 .…”

Stability of Two Weakly Coupled Elastic Beams with Partially Local Damping

“…A wave equation with local Kelvin-Voigt damping is proposed in [49], and the semigroup corresponding to the system is eventually differentiable. e behavior of slow or exponential decay is analyzed about elastic material with voids in [50]. e stability of an elastic string system with local Kelvin-Voigt damping is studied in [51].…”