[Sur la stabilisabilité des équations de la chaleur stochastiques avec bruit multiplicatif]
On démontre qu'une équation parabolique stochastique avec bruit multiplicatif sur un domaine peut être stabilisée par un contrôle agissant seulement sur un sous-domaine si est « assez petit ». On considère le cas des équations linéaires et celui des équations semi-linéaires.
We show that a stochastic heat equation with multiplicative noise on a bounded domain can be stabilized by a control acting only on a subdomain if is sufficiently ‘thin’. We consider both linear and semilinear stochastic heat equations.
Accepté le :
Publié le :
@article{CRMATH_2002__334_4_311_0,
author = {Barbu, Viorel and Lefter, Catalin and Tessitore, Gianmario},
title = {A note on the stabilizability of stochastic heat equations with multiplicative noise},
journal = {Comptes Rendus. Math\'ematique},
pages = {311--316},
publisher = {Elsevier},
volume = {334},
number = {4},
year = {2002},
doi = {10.1016/S1631-073X(02)02259-8},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02259-8/}
}
TY - JOUR AU - Barbu, Viorel AU - Lefter, Catalin AU - Tessitore, Gianmario TI - A note on the stabilizability of stochastic heat equations with multiplicative noise JO - Comptes Rendus. Mathématique PY - 2002 SP - 311 EP - 316 VL - 334 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02259-8/ DO - 10.1016/S1631-073X(02)02259-8 LA - en ID - CRMATH_2002__334_4_311_0 ER -
%0 Journal Article %A Barbu, Viorel %A Lefter, Catalin %A Tessitore, Gianmario %T A note on the stabilizability of stochastic heat equations with multiplicative noise %J Comptes Rendus. Mathématique %D 2002 %P 311-316 %V 334 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02259-8/ %R 10.1016/S1631-073X(02)02259-8 %G en %F CRMATH_2002__334_4_311_0
Barbu, Viorel; Lefter, Catalin; Tessitore, Gianmario. A note on the stabilizability of stochastic heat equations with multiplicative noise. Comptes Rendus. Mathématique, Tome 334 (2002) no. 4, pp. 311-316. doi : 10.1016/S1631-073X(02)02259-8. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02259-8/
[1] V. Barbu, A. Răşcanu, G. Tessitore, Carleman estimates and controllability of linear stochastic heat equations, Preprint della Scuola Normale, Pisa, 2001
[2] V. Barbu, G. Tessitore, Considerations on the controllability of stochastic linear heat equations, in: G. Da Prato, L. Tubaro (Eds.), Stochastic Partial Differential Equations and Applications, Marcel Dekker, 2001 (to appear)
[3] Fractional-steps method for a class of SPDEs, Stochastic Process. Appl., Volume 73 (1998), pp. 1-45
[4] Optimal stationary control with state and control dependent noise, SIAM J. Control Optim., Volume 9 (1971), pp. 184-198
[5] A note on the stability of stochastic systems with unbounded perturbations, Stochastic Anal. Appl., Volume 7 (1989), pp. 426-434
[6] E. Pardoux, Equations aux dérivées partielles stochastiques nonlinéaires monotones, étude de solutions fortes du type Itô, Thèse, Paris-Sud, Orsay, 1975
[7] M. Sirbu, G. Tessitore, Null controllability of an infinite dimensional SDE with state and control-dependent noise, Preprint, DIMA-Università di Genova, 1999
[8] Some remarks on the mean square stabilizability of a linear SPDE, Dynamic Systems Appl., Volume 2 (1993), pp. 251-266
[9] Feedback stabilizability for stochastic systems with state and control depending noise, Automatica, Volume 12 (1976), pp. 277-283
Cité par Sources :
