  Cancer is a very complex phenomenon that involves many different scales and
situations. In this paper we consider a free boundary problem describing the
evolution of a tumor colony and we derive a new asymptotic model for tumor
growth. We focus on the case of a single phase tumor colony taking into account
chemotactic effects in an early stage where there is no necrotic inner region.
Thus, our model is valid for the case of multilayer avascular tumors with very
little access to both nutrients and inhibitors or the case where the amount of
nutrients and inhibitors is very similar to the amount consumed by the
multilayer tumor cells. Our model takes the form of a single nonlocal and
nonlinear partial differential equation. Besides deriving the model, we also
prove a well-posedness result.

Analysis of PDEs;Biological Physics;Medical Physics