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
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.
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