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

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  • Jingjing Cai

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 ), 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).

Suggested Citation

  • Jingjing Cai, 2014. "Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, June.
    • Handle: RePEc:hin:jnljam:724582
    DOI: 10.1155/2014/724582
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