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.
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.
Accepted:
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Viorel Barbu 1; Catalin Lefter 1; Gianmario Tessitore 2
@article{CRMATH_2002__334_4_311_0,
author = {Viorel Barbu and Catalin Lefter and Gianmario Tessitore},
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},
}
TY - JOUR AU - Viorel Barbu AU - Catalin Lefter AU - Gianmario Tessitore 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 DO - 10.1016/S1631-073X(02)02259-8 LA - en ID - CRMATH_2002__334_4_311_0 ER -
%0 Journal Article %A Viorel Barbu %A Catalin Lefter %A Gianmario Tessitore %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 %R 10.1016/S1631-073X(02)02259-8 %G en %F CRMATH_2002__334_4_311_0
Viorel Barbu; Catalin Lefter; Gianmario Tessitore. A note on the stabilizability of stochastic heat equations with multiplicative noise. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 311-316. doi : 10.1016/S1631-073X(02)02259-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02259-8/
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