Theoretical and numerical stability results for a viscoelastic swelling porous-elastic system with past history

Abstract

The purpose of this paper is to establish a general stability result for a one-dimensional linear swelling porous-elastic system with past history, irrespective of the wave speeds of the system. First, we establish an explicit and general decay result under a wider class of the relaxation (kernel) functions. The kernel in our memory term is more general and of a broader class. Further, we get a better decay rate without imposing some assumptions on the boundedness of the history data considered in many earlier results in the literature. We also perform several numerical tests to illustrate our theoretical results. Our output extends and improves some of the available results on swelling porous media in the literature.

Keywords

• swelling porous problem
• viscoelastic
• general decay
• convex functions
• finite element and crank-nicolson methods