Formal asymptotic limit of a diffuse-interface tumor-growth model

Danielle Hilhorst (1) , Kampmann Johannes (2) , Thanh Nam Nguyen (1) , Zee Kristoffer G. van Der (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Technische Universität Dortmund, Faculty of Mathematics
3 Technische Universiteit Eindhoven, Multiscale Engineering Fluid Dynamics

We consider a diffuse-interface tumor-growth model, which has the form of a phase-field system. We discuss the singular limit of this problem. More precisely, we formally prove that as the reaction coefficient tends to zero, the solution converges to the solution of a free boundary problem.

Domaines: Equations aux dérivées partielles [math.AP]

Danielle Hilhorst, Kampmann Johannes, Thanh Nam Nguyen, Zee Kristoffer G. van Der. Formal asymptotic limit of a diffuse-interface tumor-growth model. 2013. ⟨hal-00843534⟩