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<p>This paper is concerned with a diffusive Lotka–Volterra cooperative model with population flux by attractive transition. We study the global well-posedness and the large time behavior of solutions in a case where the habitat is a bounded convex domain and random diffusion rates equal to each other. The main result shows that when the spatial dimension is less than or equal to 3, under a weaker cooperative condition, a classical solution exists globally in time if the initial data belong to a suitable functional space. Furthermore, it is shown that if there exists a positive steady state and the equal random diffusion rate is sufficiently large, then all positive solutions asymptotically approach the positive steady state as time tends to infinity.</p>

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Large time behavior of solutions to a cooperative model with population flux by attractive transition

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月10日

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  • Ryuichi Kato,
  • Kousuke Kuto

摘要

This paper is concerned with a diffusive Lotka–Volterra cooperative model with population flux by attractive transition. We study the global well-posedness and the large time behavior of solutions in a case where the habitat is a bounded convex domain and random diffusion rates equal to each other. The main result shows that when the spatial dimension is less than or equal to 3, under a weaker cooperative condition, a classical solution exists globally in time if the initial data belong to a suitable functional space. Furthermore, it is shown that if there exists a positive steady state and the equal random diffusion rate is sufficiently large, then all positive solutions asymptotically approach the positive steady state as time tends to infinity.