Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term

Jingjing Cai

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: We study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. In this model, the free boundary represents the spreading front of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomy result: spreading (the free boundary tends to +∞ and the solution converges to a stationary solution defined on [0 + ∞)), transition (the free boundary stays in a bounded interval and the solution converges to a stationary solution with positive compact support), and vanishing (the free boundary converges to 0 and the solution tends to 0 within a finite time).

Date: 2014
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https://doi.org/10.1155/2014/724582

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:724582

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