Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model
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DOI：
10.1142/s0218202520500104
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发表时间：
2019-04
影响因子：
3.5
通讯作者：
Kyudong Choi;Moon-Jin Kang;Young-Sam Kwon;A. Vasseur
中科院分区：
文献类型：
--
作者：
Kyudong Choi;Moon-Jin Kang;Young-Sam Kwon;A. Vasseur
本文考虑一类双曲抛物方程组，该方程组由具有奇异灵敏度的Keller-Segel方程描述，并由肿瘤血管生成中的趋化性模型产生。已知允许粘性冲击（所谓的行波）。我们引入了系统的相对熵，它可以捕获在给定时间的解与给定冲击波的接近程度。当激波强度足够小时，我们证明了对于任何大的初始扰动，泛函都是不随时间增加的。收缩性质与扩散的强度无关。
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 [Formula: see text]-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.