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Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation

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  • Barbu, Viorel
  • Da Prato, Giuseppe

Abstract

We prove the existence of an invariant measure [mu] for the transition semigroup Pt associated with the fast diffusion porous media equation in a bounded domain , perturbed by a Gaussian noise. The Kolmogorov infinitesimal generator N of Pt in is characterized as the closure of a second-order elliptic operator in . Moreover, we construct the Sobolev space and prove that .

Suggested Citation

  • Barbu, Viorel & Da Prato, Giuseppe, 2010. "Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1247-1266, July.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:7:p:1247-1266
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    Cited by:

    1. Ciotir, Ioana & Tölle, Jonas M., 2012. "Convergence of invariant measures for singular stochastic diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1998-2017.

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