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arXiv · 1904.12169

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

Kyudong Choi·Moon-Jin Kang·Young-Sam Kwon·Alexis Vasseur
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Abstract

We consider a hyperbolic-parabolic system arising from a chemotaxis model in 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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Kyudong Choi, Moon-Jin Kang, Young-Sam Kwon, Alexis Vasseur. 2019-04-27. Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model. https://arxiv.org/abs/1904.12169

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