Geodesic
A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth
Avner Friedman1
1Ohio State University, Columbus, USA
Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 247-261

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DOI

We consider a tumor model with three populations of cells: proliferating, quiescent, and necrotic. Cells may change from one type to another at a rate which depends on the nutrient concentration. We assume that the tumor tissue is a fluid subject to the Stokes equation with sources determined by the proliferation rate of the proliferating cells. The boundary of the tumor is a free boundary held together by cell-to-cell adhesiveness of intensity γ. Thus, on the free boundary the stress tensor T and the mean curvature κ are related by Tn=−γκn where n is the outward normal. We prove that the coupled system of PDEs for the densities of the three types of cells, the nutrient concentration, and the fluid velocity and pressure have a unique smooth solution, with a smooth free boundary, for a small time interval.
DOI : 10.4171/ifb/142
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Tumor growth, free boundary problems, hyperbolic equations, Stokes equation

Avner Friedman  1

1 Ohio State University, Columbus, USA 
Avner Friedman. A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Interfaces and free boundaries, Tome 8 (2006) no. 2, pp. 247-261. doi: 10.4171/ifb/142
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     title = {A free boundary problem for a coupled system of elliptic, hyperbolic, and {Stokes} equations modeling tumor growth},
     journal = {Interfaces and free boundaries},
     pages = {247--261},
     year = {2006},
     volume = {8},
     number = {2},
     doi = {10.4171/ifb/142},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/142/}
}
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