On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure - INRIA - Institut National de Recherche en Informatique et en Automatique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure

Résumé

Several recent papers have addressed modelling of the tissue growth by the multi-phase models where the velocity is related to the pressure by one of the physical laws (Stoke's, Brinkman's or Darcy's). While each of these models has been extensively studied, not so much is known about the connection between them. In the recent paper (arXiv:2303.10620), assuming the linear form of the pressure, the Authors connected two multi-phase models by an inviscid limit: the viscoelastic one (of Brinkman's type) and the inviscid one (of Darcy's type). Here, we prove that the same is true for a nonlinear, power-law pressure. The new ingredient is that we use relation between the pressure $p$ and the Brinkman potential $W$ to deduce compactness in space of $p$ from the compactness in space of $W$.
Fichier principal
Vignette du fichier
2306.03752.pdf (268.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04120873 , version 1 (07-06-2023)

Identifiants

Citer

Charles Elbar, Jakub Skrzeczkowski. On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure. 2023. ⟨hal-04120873⟩
20 Consultations
93 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More