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

Cai, Jingjing and Chai, Yuan and Li, Lizhen and Wu, Quanjun: Asymptotic behavior of solutions of a Fisher equation with free boundaries and nonlocal term. In: Electronic journal of qualitative theory of differential equations 79. pp. 1-18. (2019)

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Abstract

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 u0 = σφ, that is, there exists σ ∗ > 0 such that spreading happens when σ > σ , and vanishing happens when σ ≤ σ

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 79
ISSN: 1417-3875
Page Range: pp. 1-18
DOI: https://doi.org/10.14232/ejqtde.2019.1.79
Uncontrolled Keywords: Fisher-egyenlet, Differenciaegyenlet
Additional Information: Bibliogr.: p. 17-18. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 27. 12:30
Last Modified: 2020. Jan. 27. 12:30
URI: http://acta.bibl.u-szeged.hu/id/eprint/64723

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