THEORETICAL AND COMPUTATIONAL DECAY RESULTS FOR A MEMORY TYPE WAVE EQUATION WITH VARIABLE-EXPONENT NONLINEARITY

Adel M. Al-Mahdi; Mohammad M. Al-Gharabli; Mostafa Zahri

doi:10.3934/mcrf.2022010

THEORETICAL AND COMPUTATIONAL DECAY RESULTS FOR A MEMORY TYPE WAVE EQUATION WITH VARIABLE-EXPONENT NONLINEARITY

Adel M. Al-Mahdi^*
, Mohammad M. Al-Gharabli
, Mostafa Zahri

^*Corresponding author for this work

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

12 Scopus citations

Abstract

In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.

Original language	English
Pages (from-to)	605-630
Number of pages	26
Journal	Mathematical Control and Related Fields
Volume	13
Issue number	2
DOIs	https://doi.org/10.3934/mcrf.2022010
State	Published - Jun 2023

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© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Wave equations
convexity
decay
finite element method
infinite memory

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.3934/mcrf.2022010

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abstract = "In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.",

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AU - Zahri, Mostafa

PY - 2023/6

Y1 - 2023/6

N2 - In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.

AB - In this paper we are concerned with a viscoelastic wave equation with infinite memory and nonlinear frictional damping of variable-exponent type. First, we establish explicit and general decay results with a very general assumption on the relaxation function. Then, we remove the constraint imposed on the boundedness condition on the initial data used in the earlier results in the literature. Finally, we perform several numerical tests to illustrate our theoretical findings. This study generalizes and improves previous literature outcomes.

KW - Wave equations

KW - convexity

KW - decay

KW - finite element method

KW - infinite memory

UR - https://www.scopus.com/pages/publications/85145831805

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IS - 2

ER -

THEORETICAL AND COMPUTATIONAL DECAY RESULTS FOR A MEMORY TYPE WAVE EQUATION WITH VARIABLE-EXPONENT NONLINEARITY

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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