  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.
