21 mar 2012 -- 17:00 [open in google calendar]
Sala Seminari, Department of Mathematics, Pisa University
The Perona-Malik equation is the prototype of forward-backward parabolic PDEs. Despite of the ill-posedness from the analytical point of view, numerical simulations seem to show much more stability than expected. In particular, evolutions of approximating schemes seem to happen in three different time scales (called fast time, standard time, and slow time), whose existence is almost independent of the approximating model.
This talk is concerned with this phenomenology, and with some possible approaches to a mathematically rigorous explanation.
(The talk is based on some joint works with M. Colombo and M. Ghisi)