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Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise. (English) Zbl 1283.35062

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.

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
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