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

作者：Djouamai Leila; Said Houari Belkacem^*

来源：Journal of Mathematical Analysis and Applications, 2014, 409(2): 705-715.

DOI：10.1016/j.jmaa.2013.07.049

• Decay rate
• Stability
• Regularity-loss
• Regularity gain
• Energy method

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) 171 L1 (R). Furthermore, we prove that by restricting the initial data to be in Hs (R) boolean AND L1-gamma (R) and gamma E 10, 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.

• 出版日期2014-1-15