Nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Chae, Myeongju¹  Choi, Kyudong² 

[1] Hankyong Univ, Dept Math, Jungang Ro 327, Anseong 17579, Gyeonggi Do, South Korea

[2] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Gil 50, Ulsan 44919, South Korea

关键词: Tumor angiogenesis;    Chemotaxis;    Nonlinear stability;    2D infinite cylinder;    Planar traveling wave;    Chemical diffusion;   

DOI  :  10.1016/j.jde.2019.09.061

来源: Elsevier

【 摘 要 】

We consider a simplified chemotaxis model of tumor angiogenesis, described by a Keller-Segel system on the two dimensional infinite cylindrical domain (x, y) is an element of R x S-lambda, where S-lambda is the circle of perimeter lambda > 0. The domain models a virtual channel where newly generated blood vessels toward the vascular endothelial growth factor will be located. The system is known to allow planar traveling wave solutions of an invading type. In this paper, we establish the nonlinear stability of these traveling invading waves when chemical diffusion is present if lambda is sufficiently small. The same result for the corresponding system in one-dimension was obtained by Li-Li-Wang (2014) [17]. Our result solves the problem remained open in Chae-Choi-Kang-Lee (2018) [3] at which only linear stability of the planar traveling waves was obtained under certain artificial assumption. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free