Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion. (29th March 2016) - Li, Yan; Lankeit, Johannes
Abstract: This article deals with an initial-boundary value problem for the coupled chemotaxis–haptotaxis system with nonlinear diffusion under homogeneous Neumann boundary conditions in a bounded smooth domain, n = 2, 3, 4, where and μ are given nonnegative parameters. The diffusivity D ( u ) is assumed to satisfy for all u > 0 with some . It is proved that for sufficiently regular initial data global bounded solutions exist whenever . For the case of non-degenerate diffusion (i.e. D (0) > 0) the solutions are classical; for the case of possibly degenerate diffusion ( ), the existence of bounded weak solutions is shown.