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

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 e...

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Bibliographic Details
Published in:Journal of Differential Equations 2020-03, Vol.268 (7), p.3449-3496
Main Authors: Chae, Myeongju, Choi, Kyudong
Format: Article
Language:English
Subjects:
2D infinite cylinder
Chemical diffusion
Chemotaxis
Nonlinear stability
Planar traveling wave
Tumor angiogenesis
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.09.061