| Issue |
ESAIM: COCV
Volume 19, Number 4, October-December 2013
|
|
|---|---|---|
| Page(s) | 1055 - 1063 | |
| DOI | https://doi.org/10.1051/cocv/2012044 | |
| Published online | 04 July 2013 | |
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative Gaussian noise∗
Al.I. Cuza University and Octav Mayer Institute of Mathematics
(Romanian Academy), Blvd. Carol I,
No. 11, 700506
Iaşi,
Romania
vbarbu41@gmail.com
Received: 26 April 2012
Revised: 3 November 2012
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.
Mathematics Subject Classification: 35Q30 / 60H15 / 35B40
Key words: Stochastic equation / brownian motion / Navier − Stokes equation / feedback controller
© EDP Sciences, SMAI, 2013
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