SEMINARIO DI MATEMATICA
Ore 15.00
Scuola Normale
Superiore
Pisa
(Aula Bianchi)
Prof. Michael Roeckner
Terrà un
seminario dal titolo:
“Recent
extinction results for stochastic porous
media equations and
applications to self-organized criticality”
Abstract:
The first
part of the
talk will recall extinction
results for stochastic partial dif-
ferential equations
(with multiplicative
noise) of porous
media type. These
include stochastic fast diffusion equations
and more singular cases,
where e.g. the non- linearity
is given
by a
Heaviside or sign
function, so is multivalued. The latter
describe
certain continuum
models
for the phenomenon
of self-organized
criticality (SOC). These
extinction results
have
been obtained in
the
past two
years. In
the SOC-case, however, extinction was
only shown
if the underlying spatial domain is one-dimensional
and only with
positive
(though high) probability.
The second
part of the
talk is devoted
to very
recent
results, where
for the SOC-case
asymptotic ex-
tinction was
proved for all
spatial dimensions
and shown
to be
locally exponentially fast. One
main technique in the
proofs
is to transform the
stochastic PDE into
a deterministic PDE with
a random parameter. The
resulting deterministic PDE
is of an entirely new
type
and new
methods had to
be
invented
for its analysis.
Tutti gli
interessati sono invitati a partecipare.
Classe
di Scienze