On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

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

Résumé

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.
Fichier principal
Vignette du fichier
rigorous-derivation_HAL.pdf (215.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02195572 , version 1 (26-07-2019)

Identifiants

Citer

Mohamed Khaladi, Nisrine Outada, Nicolas Vauchelet. On the Hilbert Method in the Kinetic Theory of Multicellular Systems: Hyperbolic Limits and Convergence Proof. 2019. ⟨hal-02195572⟩
55 Consultations
67 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More