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.

中文翻译：

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由趋化性模型引起的双曲抛物线系统中行波大扰动的收缩

我们考虑由肿瘤血管生成中的趋化性模型产生的双曲线-抛物线系统，该模型由具有奇异敏感性的 Keller-Segel 方程描述。已知允许粘性冲击（所谓的行波）。我们引入了系统的相对熵，它可以在几乎 [公式：参见文本] 意义上捕捉给定时间的解与给定冲击波的接近程度。当冲击强度足够小时，我们表明对于任何大的初始扰动，函数都不会及时增加。收缩特性与扩散强度无关。