Convergence of invariant measures for singular stochastic diffusion equations

Ioana Ciotir and Jonas M. Tölle

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1998-2017

Abstract: It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established.

Keywords: Stochastic evolution equation; Stochastic diffusion equation; p-Laplace equation; 1-Laplace equation; Total variation flow; Fast diffusion equation; Ergodic semigroup; Unique invariant measure; Variational convergence (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2011.11.011

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