What we know about the two-phase Stefan problem under minimal assumptions

PDE Seminar
Tuesday, March 3, 2009 - 15:05
1.5 hours (actually 80 minutes)
Skiles 255
Kansas State University, Manhattan
In this talk I will describe recent work with C. N. Moore about the two-phase Stefan problem with a degenerate zone. We start with local solutions (no reference to initial or boundary data) and then obtain intrinsic energy estimates, that will in turn lead to the continuity of the temperature. We then show existence and uniqueness of solutions with signed measures as data. The uniqueness problem with signed measure data has been open for some 30 years for any degenerate parabolic equation.