Abstract
A model describing the growth of necrotic tumors in different regimes of vascularisation is studied. The tumor consists of a necrotic core of death cells and a surrounding shell which contains life-proliferating cells. The blood supply provides the nonnecrotic region with nutrients and no inhibitor chemical species are present. The corresponding mathematical formulation is a moving boundary problem since both boundaries delimiting the nonnecrotic shell are allowed to evolve in time. We determine all radially symmetric stationary solutions and reduce the moving boundary problem into a nonlinear evolution equation for the functions parameterising the boundaries of the shell. Parabolic theory provides a suitable context for proving local well-posedness of the problem for small initial data.
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Escher, J., Matioc, AV., Matioc, BV. (2011). Analysis of a Mathematical Model Describing Necrotic Tumor Growth. In: Stephan, E., Wriggers, P. (eds) Modelling, Simulation and Software Concepts for Scientific-Technological Problems. Lecture Notes in Applied and Computational Mechanics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20490-6_10
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DOI: https://doi.org/10.1007/978-3-642-20490-6_10
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