A note for global existence of a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant. (31st August 2018)

• Record Type: Journal Article
• Authors: Ke, Yuanyuan; Zheng, Jiashan
• Is Part Of: Nonlinearity. Volume 31:Number 10(2018:Oct.)
• Page Start: 4602
• Page End: 4620
• Publication Date: 2018-08-31
• Subjects: chemotaxis–haptotaxis -- global existence -- non-diffusible attractant; 92C17 -- 35K55 -- 35K59 -- 35K20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aad307
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we study the following coupled chemotaxis–haptotaxis model with remodeling of non-diffusible attractant in a bounded smooth domain with zero-flux boundary conditions, where χ, ξ and η are positive parameters. Under appropriate regularity assumptions on the initial data, by developing some L p -estimate techniques, we prove the global existence and uniqueness of classical solutions when, where μ is the logistic growth rate of cancer cells. This result removes the additional restriction on μ, where μ is sufficiently large in Pang and Wang (2017 J. Differ. Equ . 263 1269–92) for the global existence of solutions.