Existence and blow up for viscoelastic hyperbolic equations with variable exponents
In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then w...
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| Language: | English |
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AIMS Press
2024-10-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024032 |
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| author | Ying Chu Bo Wen Libo Cheng |
| author_facet | Ying Chu Bo Wen Libo Cheng |
| author_sort | Ying Chu |
| collection | DOAJ |
| description | In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then we prove that a solution blows up in finite time with positive initial energy as well as nonpositive initial energy. |
| format | Article |
| id | doaj-art-917edd4eeed543f8b3cebc5d74a9d122 |
| institution | Kabale University |
| issn | 2836-3310 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-917edd4eeed543f8b3cebc5d74a9d1222025-01-23T07:55:55ZengAIMS PressCommunications in Analysis and Mechanics2836-33102024-10-0116471773710.3934/cam.2024032Existence and blow up for viscoelastic hyperbolic equations with variable exponentsYing Chu0Bo Wen1Libo Cheng2School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, 130022, ChinaSchool of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, 130022, ChinaSchool of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, 130022, ChinaIn this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo$ - $Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents $ m(x) $ and $ p(x) $. Then we prove that a solution blows up in finite time with positive initial energy as well as nonpositive initial energy.https://www.aimspress.com/article/doi/10.3934/cam.2024032variable exponentsweak solutionsviscoelasticexistenceblow up |
| spellingShingle | Ying Chu Bo Wen Libo Cheng Existence and blow up for viscoelastic hyperbolic equations with variable exponents Communications in Analysis and Mechanics variable exponents weak solutions viscoelastic existence blow up |
| title | Existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| title_full | Existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| title_fullStr | Existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| title_full_unstemmed | Existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| title_short | Existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| title_sort | existence and blow up for viscoelastic hyperbolic equations with variable exponents |
| topic | variable exponents weak solutions viscoelastic existence blow up |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2024032 |
| work_keys_str_mv | AT yingchu existenceandblowupforviscoelastichyperbolicequationswithvariableexponents AT bowen existenceandblowupforviscoelastichyperbolicequationswithvariableexponents AT libocheng existenceandblowupforviscoelastichyperbolicequationswithvariableexponents |