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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
*
afriedman@mbi.osu.edu
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Abstract

The present paper introduces a tumormodel with two time scales, the time t during which the tumorgrows and the cycle time of individual cells. The model alsoincludes the effects of gene mutations on the population densityof the tumor cells. The model is formulated as a free boundaryproblem for a coupled system of elliptic, parabolic and hyperbolicequations within the tumor region, with nonlinear and nonlocalterms. Existence and uniqueness theorems are proved, andproperties 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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