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

Jingjing Cai | Zendy

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

Author(s) -

Jingjing Cai

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/724582

Subject(s) - stefan problem , boundary (topology) , bounded function , trichotomy (philosophy) , reaction–diffusion system , algorithm , mathematics , mathematical analysis , philosophy , linguistics

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)

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