Geodesic
Derivation of a Hele–Shaw type system from a cell model with active motion
Benoît Perthame1 ; Fernando Quirós2 orcid ; Min Tang3 ; Nicolas Vauchelet1
1Université Pierre et Marie Curie, Paris, France
2Universidad Autónoma de Madrid, Spain
3Shanghai Jiao Tong University, China
Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 489-508

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DOI

We formulate a Hele–Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is considered here as a standard diffusion process. The free boundary model is derived from a description at the cell level using the asymptotic of a stiff pressure limit.
DOI : 10.4171/ifb/327
Classification : 35-XX, 76-XX, 92-XX
Mots-clés : Tumor growth, Hele–Shaw equation, porous medium equation, free boundary problems

Benoît Perthame  1   ; Fernando Quirós  2   ; Min Tang  3   ; Nicolas Vauchelet  1

1 Université Pierre et Marie Curie, Paris, France
2 Universidad Autónoma de Madrid, Spain
3 Shanghai Jiao Tong University, China 
Benoît Perthame; Fernando Quirós; Min Tang; Nicolas Vauchelet. Derivation of a Hele–Shaw type system from a cell model with active motion. Interfaces and free boundaries, Tome 16 (2014) no. 4, pp. 489-508. doi: 10.4171/ifb/327
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     title = {Derivation of a {Hele{\textendash}Shaw} type system from a cell model with active motion},
     journal = {Interfaces and free boundaries},
     pages = {489--508},
     year = {2014},
     volume = {16},
     number = {4},
     doi = {10.4171/ifb/327},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/327/}
}
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