| Abstract: |
| In this talk 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.
(Joint work with Joachim Escher, Hanover) |
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