Decay result in a problem of a nonlinearly damped wave equation with variable exponent

Mohammad Kafini; Jamilu Hashim Hassan; Mohammad M. Al-Gharabli

doi:10.3934/math.2022170

Decay result in a problem of a nonlinearly damped wave equation with variable exponent

Mohammad Kafini^*
, Jamilu Hashim Hassan
, Mohammad M. Al-Gharabli

^*Corresponding author for this work

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

2 Scopus citations

Abstract

In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.

Original language	English
Pages (from-to)	3067-3082
Number of pages	16
Journal	AIMS Mathematics
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/math.2022170
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 the Author(s), licensee AIMS Press.

Keywords

General decay
Logarithmic nonlinearity
Relaxation function
Variable exponent
Viscoelasticity

ASJC Scopus subject areas

General Mathematics

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10.3934/math.2022170

Cite this

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title = "Decay result in a problem of a nonlinearly damped wave equation with variable exponent",

abstract = "In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.",

keywords = "General decay, Logarithmic nonlinearity, Relaxation function, Variable exponent, Viscoelasticity",

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AU - Hassan, Jamilu Hashim

AU - Al-Gharabli, Mohammad M.

PY - 2022

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AB - In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.

KW - General decay

KW - Logarithmic nonlinearity

KW - Relaxation function

KW - Variable exponent

KW - Viscoelasticity

UR - https://www.scopus.com/pages/publications/85119694113

U2 - 10.3934/math.2022170

DO - 10.3934/math.2022170

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ER -

Decay result in a problem of a nonlinearly damped wave equation with variable exponent

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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