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We consider the Neumann problem for a coupled chemotaxis-haptotaxis model ofcancer invasion with/without kinetic source in a 2D bounded and smooth domain.For a large class of cell kinetic sources including zero source andsub-logistic sources, we detect an explicit condition involving the chemotacticstrength, the asymptotic "damping" rate, and the initial mass of cells toensure uniform-in-time boundedness for the corresponding Neumann problem. Ourfinding significantly improves existing 2D global existence and boundedness inrelated chemotaxis-/haptotaxis systems.

A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source