We consider several simple models of tumor growth, described by systems of PDEs, and describe results on existence of solutions and on their asymptotic behavior. The boundary of the tumor region is a free boundary. In §1 the model assumes three types of cells, proliferating, quiescent and necrotic, and the corresponding PDE system consists of elliptic, parabolic and hyperbolic equations. The model in §2 assumes that the tumor has only proliferating cells. Finally in §3 we consider a model for treatment of tumor, described by a system of elliptic and hyperbolic equations.
@article{RLIN_2004_9_15_3-4_161_0,
author = {Avner Friedman},
title = {Free boundary problems arising in tumor models},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {15},
year = {2004},
pages = {161-168},
zbl = {1162.35460},
mrnumber = {2148876},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_3-4_161_0}
}
Friedman, Avner. Free boundary problems arising in tumor models. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 161-168. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_3-4_161_0/
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