Geodesic
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1055-1063

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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.

DOI : 10.1051/cocv/2012044
Classification : 35Q30, 60H15, 35B40
Keywords: stochastic equation, brownian motion, Navier − Stokes equation, feedback controller 
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     author = {Barbu, Viorel},
     title = {Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1055--1063},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {4},
     year = {2013},
     doi = {10.1051/cocv/2012044},
     mrnumber = {3182680},
     zbl = {1283.35062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012044/}
}
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Barbu, Viorel. Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1055-1063. doi: 10.1051/cocv/2012044

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