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| We investigate a free boundary problem modeling the growth of tumors cells. The model is given by a multi-phase flow and the tumor is described as a growing continuum $\Omega$ with boundary $\partial \Omega$ both of which evolve in time. In particular the model consists of a nonlinear second-order parabolic equations describing the diffusion of nutrient, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation. |
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