Stability of solutions to stochastic partial differential equations

Benjamin Gess, Jonas M. Tölle*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as the subdifferential of a convex function and prove continuous dependence of the solutions with regard to random Mosco convergence of the convex potentials. In particular, we identify the concept of stochastic variational inequalities (SVI) as a well-suited framework to study such stability properties. The generality of the developed framework is then laid out by deducing Trotter type and homogenization results for stochastic fast diffusion and stochastic singular p-Laplace equations. In addition, we provide an SVI treatment for stochastic nonlocal p-Laplace equations and prove their convergence to the respective local models.

Original languageEnglish
Pages (from-to)4973-5025
Number of pages53
JournalJournal of Differential Equations
Volume260
Issue number6
DOIs
Publication statusPublished - 15 Mar 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Homogenization
  • Nonlocal stochastic partial differential equations
  • Random Mosco convergence
  • Singular-degenerate SPDE
  • Stochastic variational inequality
  • Trotter type results

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