Nagoya Mathematical Journal

On stabilization of partial differential equations by noise

Tomás Caraballo, Kai Liu, and Xuerong Mao

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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.

Article information

Nagoya Math. J., Volume 161 (2001), 155-170.

First available in Project Euclid: 27 April 2005

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35B10: Periodic solutions 35K15: Initial value problems for second-order parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]


Caraballo, Tomás; Liu, Kai; Mao, Xuerong. On stabilization of partial differential equations by noise. Nagoya Math. J. 161 (2001), 155--170.

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