A free boundary tumor model with time dependent nutritional supply

A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integro-differential equation describing the evolution of the tumor size. First the global existence and uniqueness of a transient solution is established under some general conditions. Then with additional regularity assumptions on the consumption and proliferation rates, the existence and uniqueness of steady-state solutions is obtained. Furthermore the convergence of the transient solutions toward the steady-state solution is verified. Finally the long time behavior of the solutions is investigated by transforming the time-dependent domain to a fixed domain.