Il giorno 5 luglio 2016, alle ore 11:30, presso la sala seminari del
Dipartimento di Matematica dell'Università di Pisa, si terrà il seguente
seminario:
A. Hocquet (TU Berlin): Finite-time singularities of the stochastic
harmonic map flow on surfaces.
Abstract: A ferromagnetic material possesses a magnetization, which, out
of equilibrium, satisfies the Landau-Lifshitz-Gilbert equation (LLG).
Thermal fluctuations are taken into account by Gaussian space-time white
noise.
At least in the deterministic case, there is an important parallel
between this model and the so-called Harmonic Map Flow (HMF). This was
originally used by geometers (in the early sixties) as a tool to build
harmonic maps between two manifolds u:M->N. The case where M is two
dimensional is critical, in the sense that the natural energy barely
fails to give well-posedness.
We do not address here the problem of the solvability of LLG driven by
space-time white noise. Instead, we consider a spatially correlated
version. We show that oppositely to the deterministic case, blow-up of
solutions happens no matter how we choose the initial data.
Tutti gli interessati sono invitati a partecipare.
m.