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On stabilization of partial differential equations by noise

Published online by Cambridge University Press:  22 January 2016

Tomás Caraballo ,
Kai Liu  and
Xuerong Mao
Tomás Caraballo
Affiliation:
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apartado de Correos 1160, 41080-Sevilla, Spain, caraball@cica.es
Kai Liu*
Affiliation:
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom, k.liu@swansea.ac.uk
Xuerong Mao
Affiliation:
Department of Statistics and Modelling Science, University of Strathclyde, Glasglow G1 1XH, Scotland, United Kingdom, xuerong@stams.strath.ac.uk
*
Department of Probability and Statistics, University of Sheffield, The Hicks Building, Sheffield S3 7RH, United Kingdom, K.Liu@sheffield.ac.uk
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Abstract

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Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, some stability criteria from Chow [4] and Haussmann [6] are improved and subsequently applied to certain situations, on which the original criteria commonly do not work, to ensure almost sure exponential stability. This paper also extends to infinite dimension some results due to Mao [9] on stabilization of differential equations in finite dimension.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 161 , March 2001 , pp. 155 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

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