Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

Adel M. Al-Mahdi; Mohammad Kafini; Jamilu Hashim Hassan; Mohamed Alahyane

doi:10.1007/s00033-022-01733-9

Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

Adel M. Al-Mahdi^*
, Mohammad Kafini
, Jamilu Hashim Hassan
, Mohamed Alahyane

^*Corresponding author for this work

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

9 Scopus citations

Abstract

In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.

Original language	English
Article number	94
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	73
Issue number	3
DOIs	https://doi.org/10.1007/s00033-022-01733-9
State	Published - Jun 2022

Bibliographical note

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

Keywords

Convex functions
Crank–Nicolson
Euler method
Existence
Finite difference
General decay
Porous system
Thermoelastic

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1007/s00033-022-01733-9

Cite this

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title = "Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system",

abstract = "In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.",

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author = "Al-Mahdi, \{Adel M.\} and Mohammad Kafini and Hassan, \{Jamilu Hashim\} and Mohamed Alahyane",

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T1 - Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

AU - Al-Mahdi, Adel M.

AU - Kafini, Mohammad

AU - Hassan, Jamilu Hashim

AU - Alahyane, Mohamed

PY - 2022/6

Y1 - 2022/6

N2 - In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.

AB - In this paper, we consider a one-dimensional thermoelastic porous system with memory effect. We establish the existence and uniqueness result using the Faedo Galerkin approximations method. Then, we prove a general decay result under a very general assumption on the relaxation function and for suitable initial data with enough regularities. In order to validate our theoretical results, we discretize our system using hybrid numerical scheme and we present several numerical experiments and tests.

KW - Convex functions

KW - Crank–Nicolson

KW - Euler method

KW - Existence

KW - Finite difference

KW - General decay

KW - Porous system

KW - Thermoelastic

UR - https://www.scopus.com/pages/publications/85128287967

U2 - 10.1007/s00033-022-01733-9

DO - 10.1007/s00033-022-01733-9

M3 - Article

AN - SCOPUS:85128287967

SN - 0044-2275

VL - 73

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 3

M1 - 94

ER -

Well-posedness, theoretical and numerical stability results of a memory-type porous thermoelastic system

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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