Asymptotic behavior of solutions for competitive models with a free boundary

Jian Yang

doi:10.3934/dcds.2015.35.3253

Article Contents

2015, Volume 35, Issue 7: 3253-3276. Doi: 10.3934/dcds.2015.35.3253

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Asymptotic behavior of solutions for competitive models with a free boundary

Jian Yang^1,

1.
Department of Mathematics, Tongji University, Shanghai, 200092

Received: May 31, 2014

Revised: October 31, 2014

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 35R35.

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