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

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)Hs(R)∩L1(R). Furthermore, we prove that by restricting the initial data to be in Hs(R)∩L1,γ(R)Hs(R)∩L1,γ(R) and γ∈[0,1]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.