Interface dynamics in a two-phase tumor growth model. (English) Zbl 1477.35321
Summary: 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.
MSC:
| 35R37 | Moving boundary problems for PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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