Exponential stability of mild solutions of stochastic partial differential equations with delays
作者:
Tomás Caraballo,
Kai Liu,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1999)
卷期:
Volume 17,
issue 5
页码: 743-763
ISSN:0736-2994
年代: 1999
DOI:10.1080/07362999908809633
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
A semiiinear stochastic partial differential equation with variable delays is considered. Sufficient conditions for the exponential stability in the p-th mean of mild solutions are obtained. Also, pathwise exponential stability is proved. Since the technique ofLyapunov functions is not suitable for delayed equations, the results have been proved by using the properties of the stochastic convolution. As the sufficient conditions obtained are also valid for the case without delays, one can ensure exponential stability of mild solution in some cases where the sufficient conditions in Ichikawa [11] do not give any answer. The results are illustrated with some examples
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