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.
Keywords: stochastic equation, brownian motion, Navier − Stokes equation, feedback controller
@article{COCV_2013__19_4_1055_0,
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},
year = {2013},
publisher = {EDP Sciences},
volume = {19},
number = {4},
doi = {10.1051/cocv/2012044},
mrnumber = {3182680},
zbl = {1283.35062},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2012044/}
}
TY - JOUR AU - Barbu, Viorel TI - Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1055 EP - 1063 VL - 19 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2012044/ DO - 10.1051/cocv/2012044 LA - en ID - COCV_2013__19_4_1055_0 ER -
%0 Journal Article %A Barbu, Viorel %T Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1055-1063 %V 19 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2012044/ %R 10.1051/cocv/2012044 %G en %F COCV_2013__19_4_1055_0
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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