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

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Hilhorst, Danielle, Kampmann, Johannes, 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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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0218202515500268

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

RIS ID:

https://nottingham-repository.worktribe.com/output/743567

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 > Faculty of Science > School of Mathematical Sciences

Identification Number:

https://doi.org/10.1142/S0218202515500268

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