Decay property of regularity-loss type for solutions in elastic solids with voids

Abstract
In this paper, we consider the Cauchy problem for a system of elastic solids with voids. First, we show that a linear porous dissipation leads to decay rates of regularity-loss type of the solution. We show some decay estimates for initial data in Hs(R)∩L1(R). Furthermore, we prove that by restricting the initial data to be in Hs(R)∩L1,γ(R) and γ. ∈. [0, 1], we can derive faster decay estimates of the solution. Second, we show that by adding a viscoelastic damping term, then we gain the regularity of the solution and obtain the optimal decay rate. © 2013 Elsevier Ltd.

Citation
Djouamai, L., & Said-Houari, B. (2014). Decay property of regularity-loss type for solutions in elastic solids with voids. Journal of Mathematical Analysis and Applications, 409(2), 705–715. doi:10.1016/j.jmaa.2013.07.049

Publisher
Elsevier BV

Journal
Journal of Mathematical Analysis and Applications

DOI
10.1016/j.jmaa.2013.07.049

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