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. Copyright © Cambridge University Press 2012.
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License of this version: | Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
Publication type: | Article |
Publishing status: | publishedVersion |
Publication date: | 2013 |
Keywords english: | Classical solution, Radially symmetric stationary solution, Stability, Taxis, Tumor growth, Biophysical parameters, Cell apoptosis, Classical solutions, Far field, Healthy tissues, Mathematical formulation, Nutrient concentrations, Radially symmetric, Solid tumors, Stability properties, Stationary solutions, Steady state solution, Taxis, Tumor cells, Tumor growth, Two-phase model, Well-posed problems, Cell adhesion, Cell death, Cell proliferation, Convergence of numerical methods, Nutrients, Stability, Tumors |
DDC: | 510 | Mathematik |
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