Regularity and stability in a strongly degenerate nonlinear diffusion and haptotaxis model of cancer invasion - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Regularity and stability in a strongly degenerate nonlinear diffusion and haptotaxis model of cancer invasion

Résumé

We consider a mathematical model of cancer cell invasion of the extracellular matrix (ECM), comprising a strongly degenerate parabolic partial differential equation for the cell volume fraction, coupled with an ordinary differential equation for the ECM volume fraction. The model captures the intricate link between the dynamics of invading cancer cells and the surrounding ECM. First, migrating cells undergo haptotaxis, i.e., movement up ECM density gradients. Secondly, cancer cells degrade the ECM fibers by means of membrane-bound proteases. Finally, their migration speed is modulated by the ECM pore sizes, resulting in the saturation or even interruption of cell motility both at high and low ECM densities. The inclusion of the physical limits of cell migration results in two regimes of degeneracy of the nonlinear diffusion and haptotaxis terms. We devise specific estimates that are compatible with the strong degeneracy of the equation, focusing on the vacuum present at low ECM densities. Based on these regularity results, and associated local compactness, we prove stability of weak solutions with respect to perturbations on bounded initial data.
Fichier principal
Vignette du fichier
perthame2024regularity.pdf (352.48 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04854773 , version 1 (23-12-2024)

Identifiants

  • HAL Id : hal-04854773 , version 1

Citer

Benoît Perthame, Chiara Villa. Regularity and stability in a strongly degenerate nonlinear diffusion and haptotaxis model of cancer invasion. 2024. ⟨hal-04854773⟩
0 Consultations
0 Téléchargements

Partager

More