On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof

Mohamed Khaladi; Nisrine Outada; Nicolas Vauchelet

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arXiv · 1907.12232

On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof

Mohamed Khaladi·Nisrine Outada·Nicolas Vauchelet

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Abstract

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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Mohamed Khaladi, Nisrine Outada, Nicolas Vauchelet. 2019-07-29. On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof. https://arxiv.org/abs/1907.12232

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