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February  2004, 4(1): 115-134. doi: 10.3934/dcdsb.2004.4.115

The steady state of a maturity structured tumor cord cell population

Janet Dyson 1, , Rosanna Villella-Bressan 2, and  G.F. Webb 3,

1. 

Department of Mathematics, Mansfield College, Oxford University, Oxford, England, United Kingdom
2. 

Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padua, Italy
3. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37340, United States

Received  May 2003 Revised  July 2003 Published  November 2003

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: fixed point problem., equilibrium solutions, nonlinear first order partial differential equation, Tumor cord cell population.
Mathematics Subject Classification: 34C20, 34E13, 37G0.
Citation: Janet Dyson, Rosanna Villella-Bressan, G.F. Webb. The steady state of a maturity structured tumor cord cell population. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 115-134. doi: 10.3934/dcdsb.2004.4.115
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