Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term
We study the asymptotic behavior of solutions of a Fisher equation with free boundaries and the nonlocal term (an integral convolution in space). This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We give a d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2019-10-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7345 |
| _version_ | 1797830546738380800 |
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| author | Jingjing Cai Yuan Chai Lizhen Li Quanjun Wu |
| author_facet | Jingjing Cai Yuan Chai Lizhen Li Quanjun Wu |
| author_sort | Jingjing Cai |
| collection | DOAJ |
| description | We study the asymptotic behavior of solutions of a Fisher equation with free boundaries and the nonlocal term (an integral convolution in space). This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We give a dichotomy result, that is, the solution either converges to $1$ locally uniformly in $\mathbb{R}$, or to $0$ uniformly in the occupying domain. Moreover, we give the sharp threshold when the initial data $u_0=\sigma \phi$, that is, there exists $\sigma^*>0$ such that spreading happens when $\sigma>\sigma^*$, and vanishing happens when $\sigma\leq \sigma^*$. |
| first_indexed | 2024-04-09T13:37:50Z |
| format | Article |
| id | doaj.art-f4007ca52c064f8ba93ad47744aa5301 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:50Z |
| publishDate | 2019-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f4007ca52c064f8ba93ad47744aa53012023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-10-0120197911810.14232/ejqtde.2019.1.797345Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal termJingjing Cai0Yuan Chai1Lizhen Li2Quanjun Wu3Shanghai University of Electric Power, Shanghai, P.R. ChinaShanghai University of Electric Power, Shanghai, P.R. ChinaShanghai University of Electric Power, Shanghai, P.R. ChinaShanghai University of Electric Power, Shanghai, P.R. ChinaWe study the asymptotic behavior of solutions of a Fisher equation with free boundaries and the nonlocal term (an integral convolution in space). This problem can model the spreading of a biological or chemical species, where free boundaries represent the spreading fronts of the species. We give a dichotomy result, that is, the solution either converges to $1$ locally uniformly in $\mathbb{R}$, or to $0$ uniformly in the occupying domain. Moreover, we give the sharp threshold when the initial data $u_0=\sigma \phi$, that is, there exists $\sigma^*>0$ such that spreading happens when $\sigma>\sigma^*$, and vanishing happens when $\sigma\leq \sigma^*$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7345asymptotic behavior of solutionsfree boundary problemfisher equationnonlocal |
| spellingShingle | Jingjing Cai Yuan Chai Lizhen Li Quanjun Wu Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term Electronic Journal of Qualitative Theory of Differential Equations asymptotic behavior of solutions free boundary problem fisher equation nonlocal |
| title | Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term |
| title_full | Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term |
| title_fullStr | Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term |
| title_full_unstemmed | Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term |
| title_short | Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term |
| title_sort | asymptotic behavior of solutions of a fisher equation with free boundaries and nonlocal term |
| topic | asymptotic behavior of solutions free boundary problem fisher equation nonlocal |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7345 |
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