Connections between PDEs of porous medium type and free boundary problems

Connections between PDEs of porous medium type and free boundary problems

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Olga Turanova, IAS
Fine Hall 314

We start by describing the porous medium equation and the Hele-Shaw problem, and recalling the connection between them. Then, we present recent work linking a certain PDE system to a novel free boundary problem. The equations appearing in the latter part of the talk arise as models of tumor growth. This is joint work with Inwon Kim.