Dissipative Gradient Nonlinearities Prevent δδ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models

We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density , the chemosensitivities and the production rates of the chemoattractant and the chemorepellent . In addition, a source involving also the gradient of is incorporated. Our overall study touches on different aspects: we address questions connected to local well‐posedness, we derive sufficient conditions to ensure boundedness of solutions, and finally, we develop numerical simulations giving insights into the evolution of the system.