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ABSTRACT 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.
Li et al. (Sat,) studied this question.