Synchronization in stochastic pde systems

Wednesday, October 24, 2012 - 11:30am - 12:20pm
Keller 3-180
Igor Chueshov (Karazin Kharkov National University)
We first consider a system of semilinear parabolic stochastic partial
differential equations with additive space-time noise on the union of
thin bounded tubular domains with interaction via interface and give
conditions which guarantee synchronized behaviour of solutions at the
level of pullback attractors. Moreover, in the case of nondegenerate
noise we obtain stronger synchronization phenomena in comparison with
analogous results in the deterministic case.
Then we deal with an abstract system of two coupled nonlinear
stochastic (infinite dimensional) equations subjected to additive white
noise type process. This kind of systems may describe various
interaction phenomena in a continuum random medium. Under suitable
conditions we prove the existence of an exponentially attracting random
invariant manifold for the coupled system which means that we can
observe (nonlinear) master-slave synchronization phenomena in the coupled
system. Several examples from Mathematical Physics are discussed.
Partially based on joint results with T. Caraballo, P. E. Kloeden,
and B. Schmalfuss.
MSC Code: