We investigate the dynamics of a class of tumor growth
models known as mixed models. The key characteristic of these type of
tumor growth models is that the different populations of cells are
continuously present everywhere in the tumor at all times. In this
work we focus on the evolution of tumor growth in the presence of
proliferating, quiescent and dead cells as well as a nutrient.
The system is given by a multi-phase flow model and the tumor is
described as a growing continuum such that both the domain occupied by the tumor as well as its boundary evolve in time. Global-in-time weak solutions
are obtained using an approach based on penalization of the boundary
behavior, diffusion and viscosity in the weak formulation.
Further extensions will be discussed.
This is joint work with D. Donatelli.