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

Hilhorst, Danielle; Kampmann, Johannes; Nguyen, Thanh Nam; van der Zee, K.G.

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.

Citation

Hilhorst, D., Kampmann, J., Nguyen, T. N., & van der Zee, K. (2015). Formal asymptotic limit of a diffuse-interface tumor-growth model. Mathematical Models and Methods in Applied Sciences, 25(6), https://doi.org/10.1142/S0218202515500268

• Journal Article Type: Article
• Acceptance Date: Oct 3, 2014
• Publication Date: Jan 7, 2015
• Deposit Date: Apr 7, 2016
• Publicly Available Date: Apr 7, 2016
• Journal: Mathematical Models and Methods in Applied Sciences (M3AS)
• Electronic ISSN: 0218-2025
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 6
• DOI: https://doi.org/10.1142/S0218202515500268
• 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
• Public URL: https://nottingham-repository.worktribe.com/output/743567
• Publisher URL: http://www.worldscientific.com/doi/abs/10.1142/S0218202515500268
• Related Public URLs: https://hal.archives-ouvertes.fr/hal-00843534/
• 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