Initial/boundary-value problems of tumor growth within a host tissue

Details Initial/boundary-value problems of tumor growth within a host tissue Initial/boundary-value problems of tumor growth within a host tissue

2009-11-27

arxiv.org/abs/0911.5231v2

Physics

Mathematical Physics

30 pages, 5 figures

Scientific paper

10.1007/s00285-012-0505-1

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 nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.

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