Stability of delay evolution equations with stochastic perturbations

The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction, which was proposed by V.Kolmanovskii and L.Shaikhet, is used here to investigate the stability of stochastic delay evolution eq...

Full description

Bibliographic Details
Authors: Caraballo Garrido, Tomás, Shaikhet, Leonid
Format: article
Publication Date:2014
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23713
Online Access:http://hdl.handle.net/11441/23713
https://doi.org/10.3934/cpaa.2014.13.2095
Access Level:Open access
Keyword:Method of Lyapunov functionals construction
stochastic evolution equations
exponential stability
stochastic partial di erential equations
stochastic 2D Navier-Stokes model with delays
Description
Summary:The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The general method of Lyapunov functionals construction, which was proposed by V.Kolmanovskii and L.Shaikhet, is used here to investigate the stability of stochastic delay evolution equations, in particular, for stochastic partial diff erential equations. This method had already been successfully used for functional-di fferential equations, for diff erence equations with discrete time, and for di erence equations with continuous time. It is shown that the stability conditions obtained for stochastic 2D Navier-Stokes model with delays are essentially better than the known ones.