Global existence for time-dependent damped wave equations with nonlinear memory

Mokhtar Kirane; Ahmad Z. Fino; Ahmed Alsaedi; Bashir Ahmad

doi:10.1515/anona-2023-0111

Global existence for time-dependent damped wave equations with nonlinear memory

Mokhtar Kirane
, Ahmad Z. Fino
, Ahmed Alsaedi
, Bashir Ahmad

Department of Mathematics
American University of the Middle East
King Abdulaziz University

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

6 Scopus citations

Abstract

In this article, we consider the Cauchy problem for a semi-linear wave equation with time-dependent damping and memory nonlinearity. Conditions for global existence are presented in the energy space H 1 (R n) × L 2 (R n) {H}^{1}\left({{\mathbb{R}}}^{n})\times {L}^{2}\left({{\mathbb{R}}}^{n}), n ≥ 1 n\ge 1.

Original language	British English
Article number	20230111
Journal	Advances in Nonlinear Analysis
Volume	12
Issue number	1
DOIs	https://doi.org/10.1515/anona-2023-0111
State	Published - 1 Jan 2023

Keywords

global existence
nonlinear damped wave equation

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10.1515/anona-2023-0111

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title = "Global existence for time-dependent damped wave equations with nonlinear memory",

abstract = "In this article, we consider the Cauchy problem for a semi-linear wave equation with time-dependent damping and memory nonlinearity. Conditions for global existence are presented in the energy space H 1 (R n) × L 2 (R n) \{H\}\textasciicircum{}\{1\}\textbackslash{}left(\{\{\textbackslash{}mathbb\{R\}\}\}\textasciicircum{}\{n\})\textbackslash{}times \{L\}\textasciicircum{}\{2\}\textbackslash{}left(\{\{\textbackslash{}mathbb\{R\}\}\}\textasciicircum{}\{n\}), n ≥ 1 n\textbackslash{}ge 1.",

keywords = "global existence, nonlinear damped wave equation",

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AU - Fino, Ahmad Z.

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

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Y1 - 2023/1/1

N2 - In this article, we consider the Cauchy problem for a semi-linear wave equation with time-dependent damping and memory nonlinearity. Conditions for global existence are presented in the energy space H 1 (R n) × L 2 (R n) {H}^{1}\left({{\mathbb{R}}}^{n})\times {L}^{2}\left({{\mathbb{R}}}^{n}), n ≥ 1 n\ge 1.

AB - In this article, we consider the Cauchy problem for a semi-linear wave equation with time-dependent damping and memory nonlinearity. Conditions for global existence are presented in the energy space H 1 (R n) × L 2 (R n) {H}^{1}\left({{\mathbb{R}}}^{n})\times {L}^{2}\left({{\mathbb{R}}}^{n}), n ≥ 1 n\ge 1.

KW - global existence

KW - nonlinear damped wave equation

UR - https://www.scopus.com/pages/publications/85178025664

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JO - Advances in Nonlinear Analysis

JF - Advances in Nonlinear Analysis

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ER -

Global existence for time-dependent damped wave equations with nonlinear memory

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