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arXiv · 2504.04166

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

Ryuichi Kato·Kousuke Kuto
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Abstract

This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-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. A 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 belongs 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.

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Ryuichi Kato, Kousuke Kuto. 2025-04-05. Large time behavior of solutions to a cooperative model with population flux by attractive transition. https://arxiv.org/abs/2504.04166

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