Dissipative gradient nonlinearities prevent $\hat{I}´$-formations in local and nonlocal attraction-repulsion chemotaxis models

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.