The steady state of a maturity structured tumor cord cell population

Janet Dyson; Rosanna Villella-Bressan; G.F. Webb

doi:10.3934/dcdsb.2004.4.115

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2004, Volume 4, Issue 1: 115-134. Doi: 10.3934/dcdsb.2004.4.115

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The steady state of a maturity structured tumor cord cell population

1.
Department of Mathematics, Mansfield College, Oxford University, Oxford, England
2.
Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padua
3.
Department of Mathematics, Vanderbilt University, Nashville, TN 37340

Received: April 30, 2003

Revised: June 30, 2003

Published: January 2004

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Abstract

We consider a mathematical model of a proliferating tumor cell population forming a cylindrical structure around an interior blood vessel. We analyse the equilibrium problem when cells are distinguished by maturity, radial distance from the interior vessel, and proliferative or quiescent state. We give sufficient conditions to assure the existence of a unique steady state.

Keywords:

Tumor cord cell population,
nonlinear first order partial differential equation,
equilibrium solutions,
fixed point problem.

Mathematics Subject Classification: 34C20, 34E13, 37G05.

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