Invariant Measures for Stochastic PDE's in Unbounded Domains

Details Invariant Measures for Stochastic PDE's in Unbounded Domains Invariant Measures for Stochastic PDE's in Unbounded Domains

2000-03-28

arxiv.org/abs/nlin/0003057v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, no figs

Scientific paper

10.1088/0951-7715/14/1/308

We study stochastically forced semilinear parabolic PDE's of the Ginzburg-Landau type. The class of forcings considered are white noises in time and colored smooth noises in space. Existence of the dynamics in $L^\infty$, as well as existence of an invariant measure are proven. We also show that the solutions are with high probability analytic in a strip around the real axis and give estimates on the width of that strip.

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