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 H s ( R ) ∩ L 1 ( R ) . Furthermore, we prove that by restricting the initial data to be in H s ( R ) ∩ L 1 , 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.