Interface dynamics in a two-phase tumor growth model

We study a tumor growth model in two space dimensions, where proliferation of the cells leads to expansion domain and migration surrounding normal tissues into exterior vacuum. The features moving interfaces separating tumor, tissue, prove local-in-time existence uniqueness strong solutions for their evolution starting from nearly radial initial configuration. It is assumed that has lower mobility than which line with well-known Saffman-Taylor condition viscous fingering.