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Analysis of a two-phase model describing the growth of solid tumors

Published online by Cambridge University Press:  19 September 2012

JOACHIM ESCHER  and
ANCA-VOICHITA MATIOC
JOACHIM ESCHER
Affiliation:
Institute for Applied Mathematics, Leibniz University Hanover, Welfengarten 1, 30167 Hanover, Germany emails: escher@ifam.uni-hannover.de, matioca@ifam.uni-hannover.de
ANCA-VOICHITA MATIOC
Affiliation:
Institute for Applied Mathematics, Leibniz University Hanover, Welfengarten 1, 30167 Hanover, Germany emails: escher@ifam.uni-hannover.de, matioca@ifam.uni-hannover.de
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Abstract

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.

Keywords

Radially symmetric stationary solutionClassical solutionStabilityTumor growthTaxis
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 1 , February 2013 , pp. 25 - 48
Copyright
Copyright © Cambridge University Press 2012

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