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SUMMARY:Hele-Shaw type free boundary problems as nonlinear fractional heat
  equations - Russell Schwab (Michigan State University)
DTSTART:20220221T140000Z
DTEND:20220221T143000Z
UID:TALK167681@talks.cam.ac.uk
DESCRIPTION:We will discuss a few different recent works which allow to co
 nvert some free boundary flows similar to Help-Shaw (in both one and two p
 hase situations) into a nonlinear fractional heat equation for the functio
 n whose graph represents the moving free boundary. &nbsp\;After the conver
 sion to a nonlinear fractional heat equation\, the tools of viscosity solu
 tions and Krylov-Safonov theory become applicable to give different types 
 of well-posedness and regularization results than appear with different me
 thods that treat the free boundary in its original form. &nbsp\;As the one
 -phase case is relatively well understood\, these techniques are more nove
 l for the two-phase setting. &nbsp\;This involves joints works with Abedin
 \, Chang Lara\, and Guillen.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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