Dissipative gradient nonlinearities prevent $\delta$-formations in local and nonlocal attraction-repulsion chemotaxis models

TL;DR

This paper investigates how dissipative gradient nonlinearities influence the formation of singularities in both local and nonlocal chemotaxis models with attraction and repulsion, considering complex nonlinear diffusion and signaling mechanisms.

Contribution

It introduces a framework showing that dissipative gradient nonlinearities prevent delta-formation in chemotaxis models with nonlinear diffusion and gradient-dependent sources.

Findings

Dissipative nonlinearities inhibit delta-formation.

Models with gradient nonlinearities exhibit enhanced stability.

Theoretical analysis supports prevention of singularities.

Abstract

We study some attraction repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density, and for the chemosensitivities and the production rates of the chemoattractant and the chemorepellent. Additionally, a source also involving some expression of the gradient of the species is incorporated.