Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise

Viorel Barbu

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 4, page 1055-1063
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 19.4 (2013): 1055-1063. <http://eudml.org/doc/272931>.

@article{Barbu2013,
abstract = {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.},
author = {Barbu, Viorel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stochastic equation; brownian motion; Navier − Stokes equation; feedback controller; Brownian motion; Navier-Stokes equation},
language = {eng},
number = {4},
pages = {1055-1063},
publisher = {EDP-Sciences},
title = {Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise},
url = {http://eudml.org/doc/272931},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 4
SP - 1055
EP - 1063
AB - 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.
LA - eng
KW - stochastic equation; brownian motion; Navier − Stokes equation; feedback controller; Brownian motion; Navier-Stokes equation
UR - http://eudml.org/doc/272931
ER -

References

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  9. [9] Qi, Lü, Some results on the controllability of forward stochastic heat equations with control on the drift. J. Funct. Anal.260 (2011) 832–851. Zbl1213.60105MR2737398
  10. [10] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge (2008). Zbl1140.60034MR1207136
  11. [11] D. Goreac, Approximate controllability for linear stochastic differential equations in infinite dimensions. Appl. Math. Optim.53 (2009) 105–132. Zbl1211.93020MR2511788
  12. [12] O. Imanuvilov, On exact controllability of the Navier–Stokes equations. ESAIM: COCV 3 (1998) 97–131. Zbl1052.93502MR1617825
  13. [13] R.S. Lipster and A. Shiryaev, Theory of Martingales. Kluwer Academic, Dordrecht (1989). MR1022664
  14. [14] S. Tang and X. Zhang, Null controllability for forward and backward stochastic parabolic equations. SIAM J. Control Optim.48 (2009) 2191–2216. Zbl1203.93027MR2520325

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