# Blow-up prevention by sublinear production in a n-dimensional attraction-repulsion chemotaxis system

## TL;DR

This paper proves that in an n-dimensional attraction-repulsion chemotaxis system, sublinear chemical production guarantees global bounded solutions regardless of attraction and repulsion strengths.

## Contribution

It establishes the global existence and boundedness of solutions under sublinear production, addressing an open question in chemotaxis modeling.

## Key findings

- Global classical solutions exist and are bounded with sublinear production.
- No restrictions on attraction or repulsion coefficients are needed.
- Addresses an open problem in chemotaxis systems.

## Abstract

In this paper we study a zero-flux attraction-repulsion che\-mo\-taxis-system. We show that despite any mutual interplay between the repulsive and attractive coefficients from the corresponding chemo-sensitivities, even less any restriction on their own sizes, if the production rate of that chemical signal responsible of the cellular coalescence is sublinear, then any initial data emanate a unique global classical solution, which is as well bounded. Further, in a remark of the manuscript, we also address an open question given in \cite{Viglialoro2019RepulsionAttraction}.