Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
FD2 Reunion Seminar: Hele-Shaw Solutions Beyond Graph Domains
The Hele-Shaw problem describes a flow driven by gravity in a porous medium with free boundary. It allows various formulations which are equivalent in smooth situations. We work with the formulation of Elliot and Janovsky who obtain the solution at time t as a solution to an elliptic obstacle problem.
We obtain three main results:
1) Unique solutions for an initial domain with boundary in { |x_N| < C }
2) Global smooth solutions for graph domains with x_N < h(x'), h
bounded, continuously differentiable with bounded derivative.
3) Waiting time phenomena.
A crucial tool is the boundary Harnack inequality.
Meeting ID: 998 5718 9855
Passcode: 983468
Link: https://msri.zoom.us/j/99857189855?pwd=LzRFR2tPN1cydWJNZEZkclZGV2lpQT09
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