Free Boundary Problems Associated with Multiscale Tumor Models

A. Friedman

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 3, page 134-155
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Friedman, A.. "Free Boundary Problems Associated with Multiscale Tumor Models." Mathematical Modelling of Natural Phenomena 4.3 (2009): 134-155. <http://eudml.org/doc/222390>.

@article{Friedman2009,
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. },
author = {Friedman, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {free boundary problems; system of PDEs; tumor; cell cycle; free boundary problem; tumor growth},
language = {eng},
month = {6},
number = {3},
pages = {134-155},
publisher = {EDP Sciences},
title = {Free Boundary Problems Associated with Multiscale Tumor Models},
url = {http://eudml.org/doc/222390},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Friedman, A.
TI - Free Boundary Problems Associated with Multiscale Tumor Models
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/6//
PB - EDP Sciences
VL - 4
IS - 3
SP - 134
EP - 155
AB - 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.
LA - eng
KW - free boundary problems; system of PDEs; tumor; cell cycle; free boundary problem; tumor growth
UR - http://eudml.org/doc/222390
ER -

References

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