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