# American Institute of Mathematical Sciences

July  2015, 35(7): 3253-3276. doi: 10.3934/dcds.2015.35.3253

## Asymptotic behavior of solutions for competitive models with a free boundary

 1 Department of Mathematics, Tongji University, Shanghai, 200092

Received  June 2014 Revised  November 2014 Published  January 2015

In this paper, we study a competitive model involving two species separated by a free boundary by virtue of strong competition. When the initial data has positive lower bounds near $\pm\infty$, we prove that the solution converges, as $t\rightarrow \infty$, to a traveling wave solution and the free boundary moves to infinity with a constant speed.
Citation: Jian Yang. Asymptotic behavior of solutions for competitive models with a free boundary. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3253-3276. doi: 10.3934/dcds.2015.35.3253
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