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

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

Authors

Danielle Hilhorst

Johannes Kampmann

Thanh Nam Nguyen



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), doi: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 http://eprints.nottingham.ac.uk/id/eprint/32681
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S0218202515500268
Related Public URLs https://hal.archives-ouvertes.fr/hal-00843534/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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