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

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Title
Nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogesis with chemical diffusion
Author
Chae, MyeongjuChoi, Kyudong
Issue Date
2020-03
Publisher
Academic Press
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.268, no.7, pp.3449 - 3496
Abstract
We consider a simplified chemotaxis model of tumor angiogenesis, described by a Keller-Segel system on the two dimensional infinite cylindrical domain (x,y)∈R×Sλ, where Sλ is the circle of perimeter λ>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 λ 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.
URI
https://scholarworks.unist.ac.kr/handle/201301/27779
URL
https://www.sciencedirect.com/science/article/pii/S0022039619304681?via%3Dihub
DOI
10.1016/j.jde.2019.09.061
ISSN
0022-0396
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