Barbu, Viorel Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise. (English) Zbl 1283.35062 ESAIM, Control Optim. Calc. Var. 19, No. 4, 1055-1063 (2013). Summary: The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier-Stokes equations with multiplicative noise. The exact controllability is also discussed. Cited in 5 Documents MSC: 35Q30 Navier-Stokes equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35B40 Asymptotic behavior of solutions to PDEs 93B52 Feedback control 35K55 Nonlinear parabolic equations Keywords:stochastic equation; Brownian motion; Navier-Stokes equation; feedback controller PDFBibTeX XMLCite \textit{V. Barbu}, ESAIM, Control Optim. Calc. Var. 19, No. 4, 1055--1063 (2013; Zbl 1283.35062) Full Text: DOI