Boundedness through nonlocal dampening effects in a fully parabolic chemotaxis model with sub and superquadratic growth

TL;DR

This paper investigates a chemotaxis model with nonlocal dampening effects, demonstrating that strong enough dampening prevents cell aggregation over time, especially under sub and superquadratic growth conditions.

Contribution

It introduces a novel analysis of how nonlocal dampening influences cell density behavior in chemotaxis models with complex growth effects.

Findings

No cell gathering occurs if dampening is sufficiently strong.

The model accounts for sub and superquadratic growth effects.

Dampening prevents unbounded cell aggregation over time.

Abstract

This work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the mechanism of the two densities once their initial configurations are fixed in bounded impenetrable regions; in the specific, we establish that no gathering effect for the cells can appear in time provided that the dampening effect is strong enough.