Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term
We study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. In this model, the free boundary represents the spreading front of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomy result: sprea...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/724582 |
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| _version_ | 1832548974709440512 |
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| author | Jingjing Cai |
| author_facet | Jingjing Cai |
| author_sort | Jingjing Cai |
| collection | DOAJ |
| description | We study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. In this model, the free boundary represents the spreading front of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomy result: spreading (the free boundary tends to +∞ and the solution converges to a stationary solution defined on [0+∞)), transition (the free boundary stays in a bounded interval and the solution converges to a stationary solution with positive compact support), and vanishing (the free boundary converges to 0 and the solution tends to 0 within a finite time). |
| format | Article |
| id | doaj-art-cad6e3db82e541e4a3603566ff4d4f0f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cad6e3db82e541e4a3603566ff4d4f0f2025-02-03T06:12:32ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/724582724582Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction TermJingjing Cai0School of Mathematics and Physics, Shanghai University of Electric Power, Pingliang Road 2103, Shanghai 200090, ChinaWe study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. In this model, the free boundary represents the spreading front of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomy result: spreading (the free boundary tends to +∞ and the solution converges to a stationary solution defined on [0+∞)), transition (the free boundary stays in a bounded interval and the solution converges to a stationary solution with positive compact support), and vanishing (the free boundary converges to 0 and the solution tends to 0 within a finite time).http://dx.doi.org/10.1155/2014/724582 |
| spellingShingle | Jingjing Cai Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term Journal of Applied Mathematics |
| title | Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term |
| title_full | Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term |
| title_fullStr | Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term |
| title_full_unstemmed | Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term |
| title_short | Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term |
| title_sort | asymptotic behavior of solutions of free boundary problem with logistic reaction term |
| url | http://dx.doi.org/10.1155/2014/724582 |
| work_keys_str_mv | AT jingjingcai asymptoticbehaviorofsolutionsoffreeboundaryproblemwithlogisticreactionterm |