Some refined criteria toward boundedness in an attraction-repulsion chemotaxis system with nonlinear productions

TL;DR

This paper investigates boundedness criteria in a chemotaxis system with nonlinear production, improving existing results, solving an open problem, and providing numerical simulations in two-dimensional domains.

Contribution

It offers refined criteria for boundedness in attraction-repulsion chemotaxis models with nonlinear production, advancing theoretical understanding and addressing an open question.

Findings

Improved boundedness criteria for chemotaxis models.

Resolved an open problem in the literature.

Numerical simulations support theoretical results.

Abstract

We study some zero-flux attraction-repulsion chemotaxis models, with nonlinear production rates for the chemorepellent and the chemoattractant. This paper partially improves some known results in the literature and moreover solves an open question. The research is also complemented with numerical simulations in bi-dimensional domains.