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Free BoundaryProblems Associated with Multiscale Tumor Models

Published online by Cambridge University Press:  05 June 2009

A. Friedman
A. Friedman*
Affiliation:
Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA
*
[email protected]
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Abstract

The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary are established.

Keywords

free boundary problemssystem of PDEstumorcell cycle
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 3: Cancer modelling (Part 2) , 2009 , pp. 134 - 155
Copyright
© EDP Sciences, 2009

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