Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model

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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.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2020-02
Language
English
Article Type
Article
Citation

MATHEMATICAL MODELS METHODS IN APPLIED SCIENCES, v.30, no.2, pp.387 - 437

ISSN
0218-2025
DOI
10.1142/S0218202520500104
URI
http://hdl.handle.net/10203/292360
Appears in Collection
MA-Journal Papers(저널논문)
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