Classical solutions to a moving boundary problem for an elliptic-parabolic system

Escher, Joachim

doi:10.4171/IFB/96

Interfaces and Free Boundaries

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Volume 6, Issue 2, 2004, pp. 175–193

DOI: 10.4171/IFB/96

Classical solutions to a moving boundary problem for an elliptic-parabolic system

Joachim Escher (1)

(1) Institute for Applied Mathematics, University of Hannover, D-30060, HANNOVER, GERMANY

The paper concerns a moving boundary problem for a coupled system of an elliptic and a parabolic boundary value problem. This system is applied to a model describing the growth of a homogeneous solid tumor in which the cell proliferation rate depends on the nutrient concentration only. For a large class of initial data the existence of a unique classical solution is shown.

Keywords: Moving boundary problem, tumor growth,