PDE Seminar Abstracts

Valentina-Mira Wheeler

University of Wollongong, Australia

Monday 26 October 2015, 2-3pm, Carslaw Room 829 (AGR)

University of Wollongong, Australia

Monday 26 October 2015, 2-3pm, Carslaw Room 829 (AGR)

In this talk we discuss the setting of rotationally symmetric graphs moving under mean curvature flow with a ninety degree angle condition on fixed rotationally symmetric hypersurfaces. If defined on an annular domain the graphs also enjoy an additional Dirichlet boundary condition. We give sufficient conditions for which the graphs will exist for all times, proved by ${C}^{1}$ estimates. By construction of auxiliary functions we prove that they converge to minimal graphs. In some cases we prove that the solution is asymptotically constant. We also give sufficient conditions for which the graphs lose graphicality and develop a curvature singularity at the free boundary. In this talk we will present the details of these arguments.

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