Energy solutions to the bi-harmonic parabolic equations
This study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourt...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241675 |
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| _version_ | 1832590778886520832 |
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| author | Saleh Almuthaybiri Tarek Saanouni |
| author_facet | Saleh Almuthaybiri Tarek Saanouni |
| author_sort | Saleh Almuthaybiri |
| collection | DOAJ |
| description | This study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourth-order parabolic problem, due to Payne-Sattynger. |
| format | Article |
| id | doaj-art-d7cf82b013614d86ba6ddf842fc62a61 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-d7cf82b013614d86ba6ddf842fc62a612025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912352643527310.3934/math.20241675Energy solutions to the bi-harmonic parabolic equationsSaleh Almuthaybiri0Tarek Saanouni1Department of Mathematics, College of Science, Qassim University, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Saudi ArabiaThis study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourth-order parabolic problem, due to Payne-Sattynger.https://www.aimspress.com/article/doi/10.3934/math.20241675inhomogeneous fourth-order parabolic problemnonlinear equationsglobal/non-global solutions |
| spellingShingle | Saleh Almuthaybiri Tarek Saanouni Energy solutions to the bi-harmonic parabolic equations AIMS Mathematics inhomogeneous fourth-order parabolic problem nonlinear equations global/non-global solutions |
| title | Energy solutions to the bi-harmonic parabolic equations |
| title_full | Energy solutions to the bi-harmonic parabolic equations |
| title_fullStr | Energy solutions to the bi-harmonic parabolic equations |
| title_full_unstemmed | Energy solutions to the bi-harmonic parabolic equations |
| title_short | Energy solutions to the bi-harmonic parabolic equations |
| title_sort | energy solutions to the bi harmonic parabolic equations |
| topic | inhomogeneous fourth-order parabolic problem nonlinear equations global/non-global solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241675 |
| work_keys_str_mv | AT salehalmuthaybiri energysolutionstothebiharmonicparabolicequations AT tareksaanouni energysolutionstothebiharmonicparabolicequations |