Global boundedness in a quasilinear attraction–repulsion chemotaxis model with nonlinear sensitivity

This paper considers the attraction–repulsion chemotaxis model with homogeneous Neumann boundary conditions in a smooth, bounded, convex domain. In this model, when the scaling constant is zero and the chemotactic sensitivity functions are nonlinear, we prove that this system possesses a unique global classical solution that is uniformly bounded under some assumptions; when the scaling constant is one and one of the chemotactic sensitivity functions is nonlinear, we also obtain a unique bounded global classical solution under some assumptions.