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

Hilhorst, Danielle and Kampmann, Johannes and Nguyen, Thanh Nam and van der Zee, K.G. (2015) Formal asymptotic limit of a diffuse-interface tumor-growth model. Mathematical Models and Methods in Applied Sciences (M3AS), 25 (6). pp. 1011-1043. ISSN 0218-2025

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Abstract

We consider a diffuse-interface tumor-growth model which has the form of a phase-field system. We characterize the singular limit of this problem. More precisely, we formally prove that as the coefficient of the reaction term tends to infinity, the solution converges to the solution of a novel free boundary problem. We present numerical simulations which illustrate the convergence of the diffuse-interface model to the identified sharp-interface limit.

Item Type: Article
Additional Information: Electronic version of an article published as Mathematical Models and Methods in Applied Sciences , 25, 6, 2015, 1011-1043 10.1142/S0218202515500268 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/m3as
Keywords: Reaction-diffusion system; Singular perturbation; Interface motion; Matched asymptotic expansion; Tumor-growth model; Phase-field model; Gradient flow; Stabilized Crank–Nicolson method; Convex-splitting scheme
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1142/S0218202515500268
Related URLs:
URLURL Type
https://hal.archives-ouvertes.fr/hal-00843534/UNSPECIFIED
Depositing User: van der Zee, Kristoffer
Date Deposited: 07 Apr 2016 08:05
Last Modified: 13 Sep 2016 18:35
URI: http://eprints.nottingham.ac.uk/id/eprint/32681

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