Convergence of invariant measures for singular stochastic diffusion equations

Ioana Ciotir, Jonas M. Tölle*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)

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. It is shown that the associated unique invariant measures of the ergodic semigroups converge in the weak sense (of probability measures).

Original languageEnglish
Pages (from-to)1998-2017
Number of pages20
JournalStochastic Processes and their Applications
Volume122
Issue number4
DOIs
Publication statusPublished - Apr 2012
MoE publication typeA1 Journal article-refereed

Keywords

  • 1-Laplace equation
  • Ergodic semigroup
  • Fast diffusion equation
  • p-Laplace equation
  • Stochastic diffusion equation
  • Stochastic evolution equation
  • Total variation flow
  • Unique invariant measure
  • Variational convergence

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