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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stabilization of evolution equations by noise


Author: Anna A. Kwiecinska
Journal: Proc. Amer. Math. Soc. 130 (2002), 3067-3074
MSC (2000): Primary 35K90, 37L55; Secondary 47D06
Published electronically: March 29, 2002
MathSciNet review: 1908931
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Abstract: We consider a deterministic equation of evolution

\begin{displaymath}X'(t)=AX(t)dt,\end{displaymath}

in a separable, real Hilbert space. We prove that if $A$generates a $C_0$-semigroup, then this equation can be stabilized, in terms of Lyapunov exponents, by noise.

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Additional Information

Anna A. Kwiecinska
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warszawa, Poland
Email: akwiecin@impan.gov.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06443-2
PII: S 0002-9939(02)06443-2
Received by editor(s): April 2, 2001
Received by editor(s) in revised form: June 1, 2001
Published electronically: March 29, 2002
Additional Notes: This research was partially supported by KBN grant 2 P03A 016 16
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2002 American Mathematical Society