Geodesic
Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth
Stefano Melchionna1 ; Elisabetta Rocca2
1Universität Wien, Austria
2Università degli Studi di Pavia, Italy
Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 571-590

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DOI

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 ε>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 ε goes to zero.
DOI : 10.4171/ifb/393
Classification : 35-XX, 49-XX, 92-XX
Mots-clés : Free boundary problems, diffuse interface models, sharp interface limit, Cahn–Hilliard equation, Darcy law, tumor growth

Stefano Melchionna  1   ; Elisabetta Rocca  2

1 Universität Wien, Austria
2 Università degli Studi di Pavia, Italy 
Stefano Melchionna; Elisabetta Rocca. Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth. Interfaces and free boundaries, Tome 19 (2017) no. 4, pp. 571-590. doi: 10.4171/ifb/393
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     title = {Varifold solutions of a sharp interface limit of a diffuse interface model for tumor growth},
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     pages = {571--590},
     year = {2017},
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     doi = {10.4171/ifb/393},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/393/}
}
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