Asymptotic behavior and uniqueness of traveling wave fronts in a competitive recursion system

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• 作者：Kun Li ; Jianhua Huang ; Xiong Li ; Yanli He
• 关键词：Competitive recursion system ; Traveling wave front ; Asymptotic behavior ; Uniqueness ; Upper and lower solutions
• 刊名：Zeitschrift f¨¹r angewandte Mathematik und Physik
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：67
• 期：6
• 全文大小：592 KB
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer Basel
• ISSN：1420-9039
• 卷排序：67

文摘

In this paper, we consider the asymptotic behavior and uniqueness of traveling wave fronts connecting two half-positive equilibria in a competitive recursion system. We first prove that these traveling wave fronts have the exponential decay rates at the minus/plus infinity, where for a given wave speed, there are three possible asymptotic behaviors for the first component of the wave profile at the plus infinity and the second component of the wave profile at the minus infinity, respectively. And then we use the sliding method to prove the uniqueness of traveling wave fronts for this system. Furthermore, by combining uniqueness and upper and lower solutions technique, we also give the exact decay rate of the weaker competitor under certain conditions.