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

Abstract

We consider the Neumann problem for a coupled chemotaxis–haptotaxis model of cancer invasion with/without kinetic source in a 2D bounded and smooth domain. For a large class of cell kinetic sources including zero source and sub-logistic sources, we detect an explicit condition involving the chemotactic strength, the asymptotic ‘damping’ rate, and the initial mass of cells to ensure uniform-in-time boundedness for the corresponding Neumann problem. Our finding significantly improves existing 2D global existence and boundedness in related chemotaxis–haptotaxis systems.