- journal article metadata
European Mathematical Society Publishing House
2018-01-18 23:40:01
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
19
2017
4
Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth
Stefano
Melchionna
Universität Wien, Austria
Elisabetta
Rocca
Università degli Studi di Pavia, Italy
Free boundary problems, diffuse interface models, sharp interface limit, Cahn–Hilliard equation, Darcy law, tumor growth
We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn–Hilliard–Darcy system that models tumor growth when a certain parameter $\epsilon > 0$, related to the interface thickness, tends to zero. In particular, we prove that weak solutions to the related initial boundary value problem tend to varifold solutions of a corresponding sharp interface model when $\epsilon$ goes to zero.
Partial differential equations
Calculus of variations and optimal control; optimization
Biology and other natural sciences
571
590
10.4171/IFB/393
http://www.ems-ph.org/doi/10.4171/IFB/393
1
15
2018