PDE Real Analysis Seminar

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Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2016/07/12

11:20-12:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Monika Muszkieta (Wroclaw University of Science and Technology)
The total variation flow in $H^{−s}$ (English)
[ Abstract ]
In the talk, we consider the total variation flow in the Sobolev space $H^{−s}$. We explain the motivation to study this problem in the context of image processing applications and provide its rigorous interpretation under periodic boundary conditions. Furthermore, we introduce a numerical scheme for an approximate solution to this flow which has been derived based on the primal-dual approach and discuses some issues concerning its convergence. We also show and compare results of numerical experiments obtained by application of this scheme for a simple initial data and different values of the index $s$.
This is a join work with Y. Giga.