Boundedness in a nonlinear chemotaxis-consumption model with gradient terms

TL;DR

This paper investigates a nonlinear chemotaxis-consumption model with gradient nonlinearities, nonlinear diffusion, and sensitivity, establishing conditions under which solutions remain bounded to better understand population control mechanisms.

Contribution

It introduces new conditions on model data that guarantee the boundedness of solutions in a chemotaxis-consumption system with gradient nonlinearities.

Findings

Derived conditions ensuring solution boundedness.

Analyzed the impact of gradient nonlinearities on population control.

Provided mathematical framework for boundedness in complex chemotaxis models.

Abstract

We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a dampening effect on the model, are considered. Moreover, the system is characterized by nonlinear diffusion and sensitivity terms. We derive conditions on some data of the problem so to ensure the boundedness of related solutions.