Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type
Purpose – The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain. Design/methodology/approach – For positive and bounded initial data, the authors study the initial zero-boundary value problem. Findings – The findings of this study showed the...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2022-01-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0042/full/pdf |
| _version_ | 1797791663510257664 |
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| author | Md Abu Hanif Sarkar |
| author_facet | Md Abu Hanif Sarkar |
| author_sort | Md Abu Hanif Sarkar |
| collection | DOAJ |
| description | Purpose – The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain. Design/methodology/approach – For positive and bounded initial data, the authors study the initial zero-boundary value problem. Findings – The findings of this study showed the complete extinction of a continuous weak solution at a finite time. Originality/value – The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian. |
| first_indexed | 2024-03-13T02:22:04Z |
| format | Article |
| id | doaj.art-7aa55dfff954496cad5b2897766ed56f |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:22:04Z |
| publishDate | 2022-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-7aa55dfff954496cad5b2897766ed56f2023-06-30T09:18:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142022-01-01281446010.1108/AJMS-08-2020-0042Finite extinction for a doubly nonlinear parabolic equation of fast diffusion typeMd Abu Hanif Sarkar0Department of Mathematics, Kumamoto University, Kumamoto, JapanPurpose – The purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain. Design/methodology/approach – For positive and bounded initial data, the authors study the initial zero-boundary value problem. Findings – The findings of this study showed the complete extinction of a continuous weak solution at a finite time. Originality/value – The extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0042/full/pdfDoubly nonlinear equationDegenerate and singular equationSobolev critical caseFinite time extinction |
| spellingShingle | Md Abu Hanif Sarkar Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type Arab Journal of Mathematical Sciences Doubly nonlinear equation Degenerate and singular equation Sobolev critical case Finite time extinction |
| title | Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| title_full | Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| title_fullStr | Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| title_full_unstemmed | Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| title_short | Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| title_sort | finite extinction for a doubly nonlinear parabolic equation of fast diffusion type |
| topic | Doubly nonlinear equation Degenerate and singular equation Sobolev critical case Finite time extinction |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2020-0042/full/pdf |
| work_keys_str_mv | AT mdabuhanifsarkar finiteextinctionforadoublynonlinearparabolicequationoffastdiffusiontype |