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2014 Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term
Jingjing Cai
J. Appl. Math. 2014: 1-5 (2014). DOI: 10.1155/2014/724582

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).

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Jingjing Cai. "Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term." J. Appl. Math. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/724582

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131821
MathSciNet: MR3219430
Digital Object Identifier: 10.1155/2014/724582

Rights: Copyright © 2014 Hindawi

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