http://www.cnr.it/ontology/cnr/individuo/prodotto/ID174287

Initial/boundary-value problems of tumor growth within a host tissue (Articolo in rivista)

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Initial/boundary-value problems of tumor growth within a host tissue (Articolo in rivista) (literal)

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Alternative label

Tosin, Andrea (2013)
Initial/boundary-value problems of tumor growth within a host tissue
in Journal of mathematical biology (Print)
(literal)

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Istituto per le Applicazioni del Calcolo \"M. Picone\", Consiglio Nazionale delle Ricerche (literal)

Titolo

Abstract

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori non-negativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case. © 2012 Springer-Verlag. (literal)

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