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November  2009, 12(4): 731-767. doi: 10.3934/dcdsb.2009.12.731

A model describing the growth and the size distribution of multiple metastatic tumors

Anne Devys 1, , Thierry Goudon 1, and  Pauline Lafitte 1,

1. 

Equipe-Projet SIMPAF, Centre de Recherche INRIA Lille Nord Europe, Parc Scientifique de la Haute Borne, 40, avenue Halley B.P. 70478, F-59658 Villeneuve d'Ascq cedex, France, France, France

Received  July 2008 Revised  July 2009 Published  August 2009

Cancer is one of the greatest killers in the world, particularly in western countries. A lot of the effort of the medical research is devoted to cancer and mathematical modeling must be considered as an additional tool for the physicians and biologists to understand cancer mechanisms and to determine the adapted treatments. Metastases make all the seriousness of cancer. In 2000, Iwata et al. [9] proposed a model which describes the evolution of an untreated metastatic tumors population. We provide here a mathematical analysis of this model which brings us to the determination of a Malthusian rate characterizing the exponential growth of the population. We provide as well a numerical analysis of the PDE given by the model.
Keywords: asymptotic behavior, McKendrick-Von Foerster equation, WENO scheme, relative entropy, metastatic tumors..
Mathematics Subject Classification: Primary: 35B40, 35Q80, 92C50, 65M99; Secondary: 35L5.
Citation: Anne Devys, Thierry Goudon, Pauline Lafitte. A model describing the growth and the size distribution of multiple metastatic tumors. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 731-767. doi: 10.3934/dcdsb.2009.12.731
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