Global existence of a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Pang, Peter Y. H.¹  Wang, Yifu² 

[1] Natl Univ Singapore, Dept Math, 10 Lower Kent Ridge Rd, Singapore 119076, Singapore

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

关键词: Chemotaxis;    Haptotaxis;    Cancer invasion;    Tissue remodeling;    Logistic proliferation;   

DOI  :  10.1016/j.jde.2017.03.016

来源: Elsevier

【 摘 要 】

This paper deals with the cancer invasion model {u(t) = Delta u - chi del center dot (u del v) - xi del center dot (u del w) + mu u(1 - u - w), x is an element of Omega, t > 0, u(t) = Delta v - v + u, x is an element of Omega, t > 0, w(t) = -vw + eta w(1 - w - u), x is an element of Omega, t > 0 in a bounded smooth domain Omega subset of R-2 with zero-flux boundary conditions, where chi, xi, mu and eta are positive parameters. Compared to previous mathematical studies, the novelty here lies in: first, our treatment of the full parabolic chemotaxis-haptotaxis system; and second, allowing for positive values of eta, reflecting processes with self-remodeling of the extracellular matrix. Under appropriate regularity assumptions on the initial data (u(0), v(0), w(0)), by using adapted L-p-estimate techniques, we prove the global existence and uniqueness of classical solutions when mu is sufficiently large, i.e., in the high cell proliferation rate regime. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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