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arXiv · 2102.03713

Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption

Guoqiang Ren·Tian Xiang
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Abstract

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but not necessarily convex domain $Ω\subset \mathbb{R}^n (n=2,3,4,5)$ with nonnegative initial data and homogeneous Neumann boundary data Under a smallness condition, boundedness of classical solutions and stabilization to constant equilibrium is known. Here, without any smallness condition, we show global existence and uniform-in-time boundedness of classical solutions in 2D and global existence, eventual smoothness and asymptotical behavior (in convex domains) of weak solutions in nD (n=3,4,5). Our findings also extend and improve the one-species chemotaxis-consumption model studied in relevant literature.

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Guoqiang Ren, Tian Xiang. 2021-02-19. Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption. https://arxiv.org/abs/2102.03713

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