| Autor: |
Jingjing Cai, Yuan Chai, Lizhen Li, Quanjun Wu |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2019, Iss 79, Pp 1-18 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2019.1.79 |
| Popis: |
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 $\sigma\leq \sigma^*$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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