On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof
Analysis of PDEs
2019-07-30 v1
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.
Keywords
Cite
@article{arxiv.1907.12232,
title = {On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof},
author = {Mohamed Khaladi and Nisrine Outada and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:1907.12232},
year = {2019}
}