Dissipation through combinations of nonlocal and gradient nonlinearities in chemotaxis models

TL;DR

This paper investigates chemotaxis models with nonlocal and gradient-dependent damping, showing that strong damping prevents cell aggregation over time in bounded regions.

Contribution

It introduces a new class of chemotaxis models incorporating combined nonlocal and gradient nonlinearities and analyzes their impact on cell density behavior.

Findings

Strong damping prevents cell gathering in finite time.

The model accounts for nonlocal and gradient effects in bounded regions.

No aggregation occurs under sufficiently strong damping.

Abstract

This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two densities is studied in bounded and impenetrable regions. In particular, it is seen that no gathering effect for the cells can appear in time provided that the damping impacts are sufficiently strong.