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Outline

Organizers :

H.Arai (University of Tokyo), Y.Giga (University of Tokyo/Hokkaido University)

Board Members :

H.Ishii (Waseda.U), T.Kawazoe (Keio.U), N.Kenmochi (Chiba.U), M.Sakai (Tokyo Metropolitan.U), Y.Shibata (Waseda.U), K.Mochizuki (Chuo.U), A.Miyachi(Tokyo Woman's Christian.U), M.Yamamoto (University of Tokyo)

Period :

March 22, 2007 (Wednesday) 10:30-11:30

Place :

Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Programme :

Matteo Novaga (Hokkaido University / Universita di Pisa)

TITLE:

A semidiscrete scheme for the Perona Malik equation

ABSTRACT:

We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we characterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.