Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption

TL;DR

This paper investigates a chemotaxis model where cells are attracted by a chemical signal that they produce and consume, ensuring the model's solutions remain bounded, thus contributing to the mathematical understanding of such biological systems.

Contribution

It introduces a boundedness result for a chemotaxis system with production and consumption of the chemical signal, extending previous models with different chemical evolution laws.

Findings

Boundedness of solutions established under certain conditions

Extension of previous chemotaxis models with production and consumption

Mathematical analysis supporting biological plausibility

Abstract

This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or production impacts, for those of the chemicals. In particular, herein we focus on the situation where the signal responsible of gathering tendencies for the particles' distribution is produced, while the opposite counterpart is consumed. In such a sense, this research complements two recent results, where the chemicals evolve according to different laws.