  We investigate the dynamics of a nonlinear system modeling tumor growth with
drug application. The tumor is viewed as a mixture consisting of proliferating,
quiescent and dead cells as well as a nutrient in the presence of a drug. The
system is given by a multi-phase flow model: the densities of the different
cells are governed by a set of transport equations, the density of the nutrient
and the density of the drug are governed by rather general diffusion equations,
while the velocity of the tumor is given by Darcy's equation. The domain
occupied by the tumor in this setting is a growing continuum $\Omega$ with
boundary $\partial \Omega$ both of which evolve in time. Global-in-time weak
solutions are obtained using an approach based on the vanishing viscosity of
the Brinkman's regularization. Both the solutions and the domain are rather
general, no symmetry assumption is required and the result holds for large
initial data.
