Free Boundary Problems Associated with Multiscale Tumor Models

Issue		Math. Model. Nat. Phenom. Volume 4, Number 3, 2009 Cancer modelling (Part. 2)


Page(s)		134 - 155
DOI		10.1051/mmnp/20094306
Published online		05 June 2009

Math. Model. Nat. Phenom. Vol. 4, No. 3, 2009, pp. 134-155
DOI: 10.1051/mmnp/20094306

Free Boundary Problems Associated with Multiscale Tumor Models

A. Friedman

Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA

afriedman@mbi.osu.edu

Published online: 5 June 2009

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.

Mathematics Subject Classification. 35Q80, 35R35, 92C50, 35Q30, 35F99, 35M99

Key words: free boundary problems -- system of PDEs -- tumor -- cell cycle

© EDP Sciences 2009

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