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Comptes Rendus Mathématique
Volume 334, n° 4
pages 311-316 (2002)
Doi : S1631-073X(02)02259-8
Received : 12 December 2001 ;  accepted : 17 December 2001
A note on the stabilizability of stochastic heat equations with multiplicative noise
Sur la stabilisabilité des équations de la chaleur stochastiques avec bruit multiplicatif
 

Viorel Barbu a , Catalin Lefter a, Gianmario Tessitore b
a Facultatea de matematică, Universitatea Alexandru Ioan Cuza, Iaşi, Romania 
b Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy 

Note presented by Alain Bensoussan

Abstract

We show that a stochastic heat equation with multiplicative noise on a bounded domain D can be stabilized by a control acting only on a subdomain OD if D⧹O is sufficiently ‘thin'. We consider both linear and semilinear stochastic heat equations. To cite this article: V. Barbu et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 311-316.

The full text of this article is available in PDF format.
Résumé

On démontre qu'une équation parabolique stochastique avec bruit multiplicatif sur un domaine D peut être stabilisée par un contrôle agissant seulement sur un sous-domaine O si D⧹O est « assez petit ». On considère le cas des équations linéaires et celui des équations semi-linéaires. Pour citer cet article : V. Barbu et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 311-316.

The full text of this article is available in PDF format.


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