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Asymptotic Behavior for Radially Symmetric Solutions of a Logistic Equation with a Free Boundary

    Jingjing Cai Affiliation
    ; Quanjun Wu Affiliation

Abstract

In this paper we investigate a logistic equation with a new free boundary condition appearing in ecology, we aim to describe the spreading of a new or invasive species by studying the asymptotic behavior of the radially symmetric solutions of the problem. We will obtain a trichotomy result: spreading (the solution converges to a stationary solution defined on the half–line), transition (the solution converges to a stationary solution with compact support) and vanishing (the solution converges to 0 within a finite time). Besides we can also obtain a dichotomy result (either spreading or vanishing happens). Moreover, in the spreading case, we give the sharp estimate of the asymptotic spreading speed of the free boundary.

Keyword : asymptotic behavior of solutions, logistic equation, free boundary, trichotomy result

How to Cite
Cai, J., & Wu, Q. (2017). Asymptotic Behavior for Radially Symmetric Solutions of a Logistic Equation with a Free Boundary. Mathematical Modelling and Analysis, 22(1), 21-36. https://doi.org/10.3846/13926292.2017.1258678
Published in Issue
Jan 11, 2017
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This work is licensed under a Creative Commons Attribution 4.0 International License.