Analysis of a mathematical model describing necrotic tumor growth

Details Analysis of a mathematical model describing necrotic tumor growth Analysis of a mathematical model describing necrotic tumor growth

2010-05-14

arxiv.org/abs/1005.2506v1

Mathematics

Analysis of PDEs

14 pages, 2 figures

Scientific paper

In this paper we study a model describing the growth of necrotic tumors in different regimes of vascularisation. The tumor consists of a necrotic core of death cells and a surrounding nonnecrotic shell. The corresponding mathematical formulation is a moving boundary problem where both boundaries delimiting the nonnecrotic shell are allowed to evolve in time.We determine all radially symmetric stationary solutions of the problem and reduce the moving boundary problem into a nonlinear evolution. Parabolic theory provides us the perfect context in order to show local well-posed of the problem for small initial data.

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