Uniform in time $L^\infty$-estimates for an attraction-repulsion chemotaxis system with double saturation

TL;DR

This paper establishes conditions under which an attraction-repulsion chemotaxis model with consumed signals has globally bounded solutions, providing uniform in time $L^ty$ estimates in smooth bounded domains.

Contribution

It introduces new criteria ensuring global boundedness for a chemotaxis system with attraction and repulsion effects, extending previous results to models with consumed signals.

Findings

Derived sufficient conditions for global bounded solutions

Established uniform in time $L^ty$ estimates

Applied results to bounded smooth domains

Abstract

In this paper we focus on an attraction-repulsion chemotaxis model with consumed signals, formulated in bounded and smooth domains $\Omega$ of $\R^n$, with $n\geq 2$. We derive sufficient conditions on its data yielding global and bounded classical solutions to the related zero-flux Cauchy problem.