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: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02079-7 |
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| _version_ | 1850225806996930560 |
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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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