Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
- Authors
- Choi, Kyudong; Kang, Moon-Jin; Kwon, Young-Sam; Vasseur, Alexis F.
- Issue Date
- Feb-2020
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Tumor angiogenesis; Keller-Segel; stability; contraction; traveling wave; viscous shock; relative entropy method; conservations laws
- Citation
- MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, v.30, no.2, pp 387 - 437
- Pages
- 51
- Journal Title
- MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
- Volume
- 30
- Number
- 2
- Start Page
- 387
- End Page
- 437
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/2528
- DOI
- 10.1142/S0218202520500104
- ISSN
- 0218-2025
1793-6314
- 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.
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