BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Farhan Abedin (Michigan State University) DTSTART:20201030T185000Z DTEND:20201030T195000Z DTSTAMP:20260423T004139Z UID:MPHA/18 DESCRIPTION:Title: He le-Shaw Flow and Parabolic Integro-Differential Equations\nby Farhan A bedin (Michigan State University) as part of TAMU: Mathematical Physics an d Harmonic Analysis Seminar\n\n\nAbstract\nI will present a regularization result for a special case of the two-phase Hele-Shaw free boundary proble m (a.k.a. interfacial Darcy flow)\, which models the evolution of two immi scible fluids flowing in the narrow gap between two parallel plates and su bject to an external pressure source. Assuming that the fluid interface is given by the graph of a function\, recent work of Chang-Lara\, Guillen\, and Schwab establishes the equivalence between the Hele-Shaw free boundary problem and a first-order parabolic integro-differential equation. By exp loiting this equivalence and using available regularity theory for nonloca l parabolic equations\, we show that if the gradient of the graph of the f luid interface has a Dini modulus of continuity for all times\, then the g radient must be Holder continuous. This is joint work with Russell Schwab (MSU).\n LOCATION:https://researchseminars.org/talk/MPHA/18/ END:VEVENT END:VCALENDAR