Convergence of invariant measures for singular stochastic diffusion equations
type: Item
instance of: scholarly article
title: Convergence of invariant measures for singular stochastic diffusion equations
zbMATH Open document ID: 1252.60059
author: Ioana Ciotir
author: Jonas M. Toelle
published in: Stochastic Processes and their Applications
publication date: 2012-06-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.2839
review text: For singular stochastic \(p\)-Laplace equations with \(p\in(1,2)\) and for stochastic fast diffusion equations with parameter~\(r\in(0,1)\) on a bounded open domain in \(\mathbb R^d\), with a cylindrical Wiener process, continuous dependence of solutions in mean on \(p\) and \(r\), resp., uniformly in time from \((0,T)\), in the corresponding Hilbert spaces is shown. Also continuous dependence of the unique invariant measures of the induced Markov semigroups on \(p\) and on \(r\), resp., in the topology of weak convergence is derived. For \(p=1\) and \(d=1\) or \(d=2\), using another notion of a solution, \(P\)-almost sure strong convergence of solutions for \(p\), \(p>1\), is shown for \(p\to 1\), uniformly in \([0,T]\).
reviewed by: Hans Crauel
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35K67
Mathematics Subject Classification ID: 37L40
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 6040311
zbMATH Keywords: singular stochastic equation
zbMATH Keywords: \(p\)-Laplace equation
zbMATH Keywords: stochastic fast diffusion equation
MaRDI profile type: Publication
OpenAlex ID: W2041366450
arXiv ID: 1201.2839
cites work: Q4954179
cites work: The Dirichlet problem for the total variation flow
cites work: The Cauchy problem for linear growth functionals
cites work: Q5186236
cites work: Lp approximation of variational problems in L1 and L∞
cites work: Analysis and control of nonlinear infinite dimensional systems
cites work: The Neumann Problem on Unbounded Domains of ℝdand Stochastic Variational Inequalities
cites work: Ergodicity for nonlinear stochastic equations in variational formulation
cites work: Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation
cites work: Stochastic Nonlinear Diffusion Equations with Singular Diffusivity
cites work: Stochastic porous media equations and self-organized criticality
cites work: Stochastic variational inequalities in infinite dimensional spaces
cites work: Stability of the separable solution for fast diffusion
cites work: A Trotter type result for the stochastic porous media equations
cites work: A Trotter-type theorem for nonlinear stochastic equations in variational formulation and homogenization.
cites work: Convergence of solutions for the stochastic porous media equations and homogenization
cites work: Ergodicity for Infinite Dimensional Systems
cites work: Degenerate parabolic equations
cites work: Q3726641
cites work: Ergodicity of stochastic curve shortening flow in the plane
cites work: Local solvability of a constrained gradient system of total variation
cites work: DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM
cites work: On ergodicity of some Markov processes
cites work: Q5599982
cites work: On the stochastic \(p\)-Laplace equation
cites work: Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts
cites work: Q4137839
cites work: A concise course on stochastic partial differential equations
cites work: Existence for a class of stochastic parabolic variational inequalities
cites work: On some stochastic parabolic variational inequalities
cites work: Deterministic and Stochastic Differential Equations in Hilbert Spaces Involving Multivalued Maximal Monotone Operators
cites work: Variational Analysis
cites work: An alternative derivation of the eigenvalue equation for the 1-Laplace operator
cites work: Best constant in Sobolev inequality
cites work: Q5489390
DOI: 10.1016/J.SPA.2011.11.011
description: scientific article; zbMATH DE number 6040311