General energy decay result for a viscoelastic swelling porous-elastic system

Abderrahmane Youkana; Adel M. Al-Mahdi; Salim A. Messaoudi

doi:10.1007/s00033-022-01696-x

General energy decay result for a viscoelastic swelling porous-elastic system

Abderrahmane Youkana
, Adel M. Al-Mahdi^*
, Salim A. Messaoudi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

In this paper, we consider the following viscoelastic swelling porous-elastic system {ρzztt-a1zxx-a2uxx+∫0tg(t-s)zxx(x,s)ds=0,in(0,1)×(0,∞),ρuutt-a3uxx-a2zxx=0,in(0,1)×(0,∞),and establish explicit energy decay result with a very general assumption on the behavior of g at infinity; that is g′(t)≤-k(t)H(g(t)),t≥0,where k and H are two functions satisfying some conditions mentioned in the paper. Our result substantially improves earlier related result in the literature.

Original language	English
Article number	88
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	73
Issue number	3
DOIs	https://doi.org/10.1007/s00033-022-01696-x
State	Published - Jun 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Convex functions
General decay
Swelling porous problem
Viscoelastic

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1007/s00033-022-01696-x

Cite this

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title = "General energy decay result for a viscoelastic swelling porous-elastic system",

abstract = "In this paper, we consider the following viscoelastic swelling porous-elastic system \{ρzztt-a1zxx-a2uxx+∫0tg(t-s)zxx(x,s)ds=0,in(0,1)×(0,∞),ρuutt-a3uxx-a2zxx=0,in(0,1)×(0,∞),and establish explicit energy decay result with a very general assumption on the behavior of g at infinity; that is g′(t)≤-k(t)H(g(t)),t≥0,where k and H are two functions satisfying some conditions mentioned in the paper. Our result substantially improves earlier related result in the literature.",

keywords = "Convex functions, General decay, Swelling porous problem, Viscoelastic",

author = "Abderrahmane Youkana and Al-Mahdi, \{Adel M.\} and Messaoudi, \{Salim A.\}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = jun,

doi = "10.1007/s00033-022-01696-x",

language = "English",

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journal = "Zeitschrift fur Angewandte Mathematik und Physik",

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TY - JOUR

T1 - General energy decay result for a viscoelastic swelling porous-elastic system

AU - Youkana, Abderrahmane

AU - Al-Mahdi, Adel M.

AU - Messaoudi, Salim A.

PY - 2022/6

Y1 - 2022/6

N2 - In this paper, we consider the following viscoelastic swelling porous-elastic system {ρzztt-a1zxx-a2uxx+∫0tg(t-s)zxx(x,s)ds=0,in(0,1)×(0,∞),ρuutt-a3uxx-a2zxx=0,in(0,1)×(0,∞),and establish explicit energy decay result with a very general assumption on the behavior of g at infinity; that is g′(t)≤-k(t)H(g(t)),t≥0,where k and H are two functions satisfying some conditions mentioned in the paper. Our result substantially improves earlier related result in the literature.

AB - In this paper, we consider the following viscoelastic swelling porous-elastic system {ρzztt-a1zxx-a2uxx+∫0tg(t-s)zxx(x,s)ds=0,in(0,1)×(0,∞),ρuutt-a3uxx-a2zxx=0,in(0,1)×(0,∞),and establish explicit energy decay result with a very general assumption on the behavior of g at infinity; that is g′(t)≤-k(t)H(g(t)),t≥0,where k and H are two functions satisfying some conditions mentioned in the paper. Our result substantially improves earlier related result in the literature.

KW - Convex functions

KW - General decay

KW - Swelling porous problem

KW - Viscoelastic

UR - https://www.scopus.com/pages/publications/85127770156

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DO - 10.1007/s00033-022-01696-x

M3 - Article

AN - SCOPUS:85127770156

SN - 0044-2275

VL - 73

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 3

M1 - 88

ER -

General energy decay result for a viscoelastic swelling porous-elastic system

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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