Communications on Pure and Applied Analysis (CPAA)

Travelling wave solutions of a free boundary problem for a two-species competitive model

Pages: 1065 - 1074, Volume 12, Issue 2, March 2013      doi:10.3934/cpaa.2013.12.1065

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Chueh-Hsin Chang - Department of Mathematics, National Taiwan University, National Taiwan University, Taipei, 10617, Taiwan (email)
Chiun-Chuan Chen - Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan (email)

Abstract: We study a di usive logistic system with a free boundary in ecology proposed by Mimura, Yamada and Yotsutani [10]. Motivated by the spreading-vanishing dichotomy obtained by Du and Lin [1], we suppose the spreading speed of the free boundary tends to a constant as time tends to in nity and consider the corresponding travelling wave problem. We establish the existence and uniqueness of a travelling wave solution for this free boundary problem.

Keywords:  KPP type equation, free boundary problem, travelling wave, spreading speed.
Mathematics Subject Classification:  35K57, 35C07, 35R35.

Received: August 2011;      Revised: April 2012;      Available Online: September 2012.