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 . Thus, on the free boundary the stress tensor and the mean curvature are related by where 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.
Cite this article
Avner Friedman, A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Interfaces Free Bound. 8 (2006), no. 2, pp. 247–261DOI 10.4171/IFB/142