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Choi, Kyudong
Fluids Analysis Lab
Research Interests
  • fluid equations, mathematical biology, conservation laws,

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Contraction for Large Perturbations of Traveling Waves in a Hyperbolic-Parabolic System Arising from a Chemotaxis Model

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Title
Contraction for Large Perturbations of Traveling Waves in a Hyperbolic-Parabolic System Arising from a Chemotaxis Model
Author
Choi, KyudongKang, Moon-JinKwon, Young-SamVasseur, Alexis F.
Issue Date
2020-02
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Citation
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, v.30, no.2, pp.387 - 437
Abstract
We consider a hyperbolic-parabolic system arising from a chemotaxis model in tumor angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. It is known to allow viscous shocks (so-called traveling waves). We introduce a relative entropy of the system, which can capture how close a solution at a given time is to a given shock wave in almost L-2-sense. When the shock strength is small enough, we show the functional is non-increasing in time for any large initial perturbation. The contraction property holds independently of the strength of the diffusion.
URI
https://scholarworks.unist.ac.kr/handle/201301/30452
URL
https://www.worldscientific.com/doi/abs/10.1142/S0218202520500104
DOI
10.1142/S0218202520500104
ISSN
0218-2025
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MTH_Journal Papers
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