Stability of delay evolution equations with stochastic perturbations

Tomás Caraballo; Leonid Shaikhet

doi:10.3934/cpaa.2014.13.2095

Article Contents

2014, Volume 13, Issue 5: 2095-2113. Doi: 10.3934/cpaa.2014.13.2095

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Stability of delay evolution equations with stochastic perturbations

Tomás Caraballo^1, and
Leonid Shaikhet^2,

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla
2.
Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015

Received: November 30, 2012

Revised: January 31, 2013

Published: August 2015

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Abstract

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 differential equations. This method had already been successfully used for functional-differential equations, for difference equations with discrete time, and for difference 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.

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Mathematics Subject Classification: Primary: 35K35, 60H15; Secondary: 60G52.

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References

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