Theoretical and Computational Results of a Memory-Type Swelling Porous-Elastic System

Abstract

In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the relaxation function and for suitable given data. We also perform several numerical tests to illustrate our theoretical decay results. Our results generalize and improve many earlier results in the literature.

Keywords

• porous problem
• viscoelastic
• decay
• convexity
• finite element
• Crank–Nicolson methods