  In this paper, we conduct a thorough mathematical analysis of a tumor growth
model with treatments. The model is a system describing the evolution of
metastatic tumors and the number of cells present in a primary tumor. The
former evolution is described by a linear transport equation and the latter by
an ordinary differential equation of Gompertzian type. The two dynamics are
coupled through a nonlocal boundary condition that takes into account the tumor
colonization rate. We prove an existence result where the main difficulty is to
deal with the coupling and to take into account the time discontinuities
generated by treatment terms. We also present numerical tests that highlight
the effect of different treatments.
