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<p>In this paper, we study the minimal speed selection of a nonlocal dispersal competition system with nonlinear cubic competition. We first establish the existence of traveling wave solutions and the uniqueness of spreading speeds. It is shown that the spreading speed is equal to the minimal speed of traveling wave solutions. Then, the challenging problem on linear or nonlinear selection of the minimal speed is investigated. By using the comparison principle and the decay characteristics for traveling wave solutions, we obtain general conditions for the linear or nonlinear selection of the minimal speed. Furthermore, by constructing appropriate upper solutions, some explicit conditions to determine the linear selection of the minimal speed are derived.</p>

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Minimal Speed Selection for a Nonlocal Dispersal Competition System with Nonlinear Cubic Competition

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Yan-Feng Yang,
  • Guo-Bao Zhang

摘要

In this paper, we study the minimal speed selection of a nonlocal dispersal competition system with nonlinear cubic competition. We first establish the existence of traveling wave solutions and the uniqueness of spreading speeds. It is shown that the spreading speed is equal to the minimal speed of traveling wave solutions. Then, the challenging problem on linear or nonlinear selection of the minimal speed is investigated. By using the comparison principle and the decay characteristics for traveling wave solutions, we obtain general conditions for the linear or nonlinear selection of the minimal speed. Furthermore, by constructing appropriate upper solutions, some explicit conditions to determine the linear selection of the minimal speed are derived.