Nonlinear Noise Excitation

Tuesday, January 15, 2013 - 2:00pm - 2:50pm
Keller 3-180
Davar Khoshnevisan (The University of Utah)
We present a part of an ongoing effort that attempts to understand
why solutions to many stochastic PDEs are intermittent. In particular,
we show that there is a strong sense in which large families of SPDEs
with intermittent solutions are extremely excitable. More significantly,
we show that this highly nonlinear level of noise excitation is, in a sense
dichotomous: Semidiscrete equations are nearly always far
less excitable than continuous equations. The reason for this dichotomy is also
identified, and somewhat surprisingly has to do with the structure theory
of certain topological groups. This is based on on-going work with Kunwoo Kim.
MSC Code: