Tumor growth has been modeled at the macroscopic level by using
established physical laws coupled with biological processes which are
described in a phenomenological fashion. Such models consist of a system
of PDEs in the tumor region; this region is changing in time, and thus
its boundary is a “free boundary.” In this talk, I shall introduce basic
material on free boundary problems, and then proceed to describe models
of tumor growth. I shall state results on existence theorems, the shape
of the free boundary, and on its asymptotic behavior as time goes to
infinity.
|