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Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays. (English) Zbl 1177.93075
Summary: By establishing an impulsive-integral inequality, some sufficient conditions about the exponential stability in \(p\) \((p\geq 2)\)-moment of mild solution for impulsive stochastic partial differential equation with delays are obtained. The results in T. Caraballo and K. Liu [Stochastic Anal. Appl. 17, No. 5, 743–763 (1999; Zbl 0943.60050)] and J. Luo [J. Math. Anal. Appl. 342, 753–760 (2008; Zbl 1157.60065)] are generalized and improved.

MSC:
93E03 Stochastic systems in control theory (general)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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