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Stochastic Cahn-Hilliard equation with singularities and reflections

Wednesday 30th June 2010 - 10:10 to 11:00
INI Seminar Room 1
We study the stochastic Cahn-Hilliard equation with an additive space-time white noise. We consider the physical potential with a double logarithmic singularity in -1 and +1 in a one-dimensionnal domain. Since the singularities are not strong enough to prevent the solution from going out the physical domain [-1,1], we add two reflection measures in the boundary. We show that the system has a unique invariant measure in order to obtain existence and uniqueness of stationary solution. We also prove some results about ergodicity, exponential mixing and integration by parts formula. This is a joint work with Arnaud Debussche (ENS Cachan Bretagne).
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons