General decay of solutions in one-dimensional porous-elastic system with memory

By Tijani Abdul-Aziz Apalara. Journal of Mathematical Analysis and Applications, 2017

76 citations recorded by the source corpus.

Abstract In this work we consider a one-dimensional porous-elastic system with memory effects. It is well-known that porous-elastic system with a single dissipation mechanism lacks exponential decay. In contrary, we prove that the unique dissipation given by the memory term is strong enough to exponentially stabilize the system, depending on the kernel of the memory term and the wave speeds of the system. In fact, we prove a general decay result, for which exponential and polynomial decay results are special cases. Our result is new and improves previous results in the literature.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5bcc04a1be3765e33ce8719ea7f0038387b5a164