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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 724582, 5 pages
Research Article

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

School of Mathematics and Physics, Shanghai University of Electric Power, Pingliang Road 2103, Shanghai 200090, China

Received 16 March 2014; Accepted 19 May 2014; Published 2 June 2014

Academic Editor: Junjie Wei

Copyright © 2014 Jingjing Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).