Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions
In this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023598?viewType=HTML |
| _version_ | 1797856509211705344 |
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| author | Zhanwei Gou Jincheng Shi |
| author_facet | Zhanwei Gou Jincheng Shi |
| author_sort | Zhanwei Gou |
| collection | DOAJ |
| description | In this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are specified under appropriate assumptions on the functions $ a, b, f, g, h $ and $ u_0 $.
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| first_indexed | 2024-04-09T20:41:32Z |
| format | Article |
| id | doaj.art-cddb759e2c54404d996b858e50e0866b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T20:41:32Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-cddb759e2c54404d996b858e50e0866b2023-03-30T01:33:38ZengAIMS PressAIMS Mathematics2473-69882023-03-0185118221183610.3934/math.2023598Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditionsZhanwei Gou0Jincheng Shi11. Basic Teaching Department, Guangdong Communication Polytechnic, Guangzhou 510650, China2. Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, ChinaIn this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are specified under appropriate assumptions on the functions $ a, b, f, g, h $ and $ u_0 $. https://www.aimspress.com/article/doi/10.3934/math.2023598?viewType=HTMLblow-uplower boundshigher dimensional spaces |
| spellingShingle | Zhanwei Gou Jincheng Shi Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions AIMS Mathematics blow-up lower bounds higher dimensional spaces |
| title | Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| title_full | Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| title_fullStr | Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| title_full_unstemmed | Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| title_short | Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| title_sort | blow up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions |
| topic | blow-up lower bounds higher dimensional spaces |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023598?viewType=HTML |
| work_keys_str_mv | AT zhanweigou blowupphenomenaandglobalexistencefornonlinearparabolicproblemsundernonlinearboundaryconditions AT jinchengshi blowupphenomenaandglobalexistencefornonlinearparabolicproblemsundernonlinearboundaryconditions |