多细胞系统动力学理论中的Hilbert方法：双曲极限和收敛性证明
On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof
摘要：
我们考虑一个系统的两个动力学方程建模的多细胞系统：第一个方程管理的细胞的动力学，而第二个动力学方程管理的化学引诱物的动力学。对于这个系统，我们首先证明了整体时间解的存在性。在建立一些先验估计之后，存在性的证明依赖于不动点过程。然后，我们研究了动力学系统重新标度后的双曲极限。它导致一个宏观系统的卡塔内奥类型。严格的推导是建立由于紧凑性方法。
英文摘要：
We consider a system of two kinetic equations modelling a multicellular system : The first equation governs the dynamics of cells, whereas the second kinetic equation governs the dynamics of the chemoattractant. For this system, we first prove the existence of global-in-time solution. The proof of existence relies on a fixed point procedure after establishing some a priori estimates. Then, we investigate the hyperbolic limit after rescaling of the kinetic system. It leads to a macroscopic system of Cattaneo type. The rigorous derivation is established thanks to a compactness method.
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