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radially symmetric stationary solution

European Journal of Applied Mathematics (1)

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Analysis of a two-phase model describing the growth of solid tumors
JOACHIM ESCHER, ANCA-VOICHITA MATIOC
Journal:

European Journal of Applied Mathematics / Volume 24 / Issue 1 / February 2013

Published online by Cambridge University Press:

19 September 2012, pp. 25-48
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In this paper we consider a two-phase model describing the growth of avascular solid tumors when taking into account the effects of cell-to-cell adhesion and taxis due to nutrient. The tumor is surrounded by healthy tissue which is the source of nutrient for tumor cells. In a three-dimensional context, we prove that the mathematical formulation corresponds to a well-posed problem, and find radially symmetric steady-state solutions of the problem. They appear in the regime where the rate of cell apoptosis to cell proliferation is less than the far field nutrient concentration. Furthermore, we study the stability properties of those radially symmetric equilibria and find, depending on the biophysical parameters involved in the problem, both stable and unstable regimes for tumor growth.