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

TL;DR

This paper investigates the global existence, boundedness, and asymptotic behavior of solutions in a two-species chemotaxis model with signal absorption, extending previous results to higher dimensions without smallness constraints.

Contribution

It establishes global solutions and their long-term behavior in multiple dimensions without the smallness condition, improving upon prior models.

Findings

Global existence of solutions in 2D and higher dimensions.

Uniform boundedness of classical solutions in 2D.

Asymptotic stabilization to equilibrium in convex domains.

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 $\Omega\subset \mathbb{R}^n (n=2,3,4,5)$ 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.