Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term

被引:0
作者
Cai, Jingjing [1 ]
Chai, Yuan [1 ]
Li, Lizhen [1 ]
Wu, Quanjun [1 ]
机构
[1] Shanghai Univ Elect Power, Sch Math & Phys, Pingliang Rd 2103, Shanghai 200090, Peoples R China
关键词
asymptotic behavior of solutions; free boundary problem; Fisher equation; nonlocal; TRAVELING-WAVES; STABILITY; SPEED;
D O I
10.14232/ejqtde.2019.1.79
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 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 <= sigma*.
引用
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页数:18
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