4:45 PM – 5:05 PM, Tuesday, October 16, 2018; Room: 114 McAllister bldg.

A gradient flow approach for a particular Hele-Shaw model

Alessandro Cucchi, Laboratoire MAP5, Universit´e Paris Descartes, Paris, France

The aim of this talk is to study a free boundary model of Hele-Shaw type, modified by an additional term, which describes some aspects of cell motility. We consider a particular case where the model admits a structure of gradient flow with respect to an energy functional composed of a boundary and a bulk energy. Within this particular assumption, it is possible to prove the existence of a weak solution of the free boundary problem by solving the JKO scheme related to the gradient flow. The mathematical tools presented here have been strongly inspired by a work of Felix Otto.

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