Formal asymptotic limit of a diffuse-interface tumor-growth model
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...
| Main Authors: | , , , |
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| Format: | Article |
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World Scientific
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32681/ |
| _version_ | 1848794466276605952 |
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| author | Hilhorst, Danielle Kampmann, Johannes Nguyen, Thanh Nam van der Zee, K.G. |
| author_facet | Hilhorst, Danielle Kampmann, Johannes Nguyen, Thanh Nam van der Zee, K.G. |
| author_sort | Hilhorst, Danielle |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:16:38Z |
| format | Article |
| id | nottingham-32681 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:38Z |
| publishDate | 2015 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-326812020-05-04T17:01:17Z https://eprints.nottingham.ac.uk/32681/ Formal asymptotic limit of a diffuse-interface tumor-growth model Hilhorst, Danielle Kampmann, Johannes Nguyen, Thanh Nam van der Zee, K.G. 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. World Scientific 2015-01-07 Article PeerReviewed 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 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 http://www.worldscientific.com/doi/abs/10.1142/S0218202515500268 doi:10.1142/S0218202515500268 doi:10.1142/S0218202515500268 |
| spellingShingle | 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 Hilhorst, Danielle Kampmann, Johannes Nguyen, Thanh Nam van der Zee, K.G. Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title | Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title_full | Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title_fullStr | Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title_full_unstemmed | Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title_short | Formal asymptotic limit of a diffuse-interface tumor-growth model |
| title_sort | formal asymptotic limit of a diffuse-interface tumor-growth model |
| topic | 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 |
| url | https://eprints.nottingham.ac.uk/32681/ https://eprints.nottingham.ac.uk/32681/ https://eprints.nottingham.ac.uk/32681/ |