Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion. (29th March 2016)

• Record Type: Journal Article
• Authors: Li, Yan; Lankeit, Johannes
• Is Part Of: Nonlinearity. Volume 29:Number 5(2016:May)
• Page Start: 1564
• Page End: 1595
• Publication Date: 2016-03-29
• Subjects: partial differential equations -- boundedness -- global existence -- chemotaxis -- haptotaxis; 35K55 (primary) -- 35B40 -- 92C17; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/5/1564
• Languages: English
• ISSNs: 0951-7715

Abstract

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.