Open AccessTheoretical and numerical stability results for a viscoelastic swelling porous-elastic system with past history
Author(s) -
Adel M. AlMahdi,
Mohammad M. AlGharabli,
Mohamed Alahyane
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021692
Subject(s) - swelling , viscoelasticity , stability (learning theory) , kernel (algebra) , class (philosophy) , porous medium , relaxation (psychology) , mathematics , term (time) , porosity , mechanics , mathematical analysis , materials science , computer science , physics , pure mathematics , composite material , psychology , artificial intelligence , social psychology , quantum mechanics , machine learning
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.