Contents Online
Methods and Applications of Analysis
Volume 22 (2015)
Number 1
Global existence and decay property for solutions in nonlinear elastic solids with voids
Pages: 101 – 130
DOI: https://dx.doi.org/10.4310/MAA.2015.v22.n1.a4
Author
Abstract
In this paper, we consider a nonlinear Cauchy problem for a system of elastic solids with voids. First, we prove that the damping in the porous equation alone is weak and the solutions of the corresponding system are of regularity-loss type. In addition, we show a global existence result for solutions in $H^s (\mathbb{R})$ for large $s$. Second, we prove that by considering an additional viscoelastic damping, then the solutions can gain some regularity and all solutions in $H^s$ with $s \geq 4$ are global in time.
Keywords
decay rate, stability, regularity-loss, regularity gain, energy method
2010 Mathematics Subject Classification
35B35, 35L55, 74D05, 93D15, 93D20
Published 1 April 2015