Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay

Abstract In this work, we investigate the logarithmic nonlinear wave equation, which is distinguished by strong time-varying delay components, infinite memory, and strong damping. Through semigroup theory, we have established a local existence result, paving the way for a comprehensive understanding...

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Main Authors: Luqman Bashir, Jianghao Hao, Salah Boulaaras, Muhammad Fahim Aslam, Tong Zhang
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Boundary Value Problems
Subjects:
Online Access:https://doi.org/10.1186/s13661-025-02079-7
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author Luqman Bashir
Jianghao Hao
Salah Boulaaras
Muhammad Fahim Aslam
Tong Zhang
author_facet Luqman Bashir
Jianghao Hao
Salah Boulaaras
Muhammad Fahim Aslam
Tong Zhang
author_sort Luqman Bashir
collection DOAJ
description Abstract In this work, we investigate the logarithmic nonlinear wave equation, which is distinguished by strong time-varying delay components, infinite memory, and strong damping. Through semigroup theory, we have established a local existence result, paving the way for a comprehensive understanding of the equation’s behavior. In addition, we explore the global existence of solutions, revealing fascinating decay results and investigating the circumstances in which blow-up may occur in solutions with negative starting energy. Our results shed light on the complex nature of this dynamic system while also strengthening the theoretical framework.
format Article
id doaj-art-d2aa44089b324a489394ecf10dcc941b
institution OA Journals
issn 1687-2770
language English
publishDate 2025-06-01
publisher SpringerOpen
record_format Article
series Boundary Value Problems
spelling doaj-art-d2aa44089b324a489394ecf10dcc941b2025-08-20T02:05:14ZengSpringerOpenBoundary Value Problems1687-27702025-06-012025112710.1186/s13661-025-02079-7Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delayLuqman Bashir0Jianghao Hao1Salah Boulaaras2Muhammad Fahim Aslam3Tong Zhang4School of Mathematics and Statistics, Shanxi UniversitySchool of Mathematics and Statistics, Shanxi UniversityDepartment of Mathematics, College of Science, Qassim UniversitySchool of Mathematics and Statistics, Shanxi UniversitySchool of Mathematics and Statistics, Shanxi UniversityAbstract In this work, we investigate the logarithmic nonlinear wave equation, which is distinguished by strong time-varying delay components, infinite memory, and strong damping. Through semigroup theory, we have established a local existence result, paving the way for a comprehensive understanding of the equation’s behavior. In addition, we explore the global existence of solutions, revealing fascinating decay results and investigating the circumstances in which blow-up may occur in solutions with negative starting energy. Our results shed light on the complex nature of this dynamic system while also strengthening the theoretical framework.https://doi.org/10.1186/s13661-025-02079-7Wave equationExponential decayLogarithmic source termStrong time-varying delayInfinite memoryStrong damping
spellingShingle Luqman Bashir
Jianghao Hao
Salah Boulaaras
Muhammad Fahim Aslam
Tong Zhang
Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
Boundary Value Problems
Wave equation
Exponential decay
Logarithmic source term
Strong time-varying delay
Infinite memory
Strong damping
title Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
title_full Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
title_fullStr Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
title_full_unstemmed Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
title_short Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay
title_sort exponential decay and blow up results of a logarithmic nonlinear wave equation having infinite memory and strong time varying delay
topic Wave equation
Exponential decay
Logarithmic source term
Strong time-varying delay
Infinite memory
Strong damping
url https://doi.org/10.1186/s13661-025-02079-7
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