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Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays. (English) Zbl 1157.60065
The exponential stability in the $$p$$-th mean and the exponential pathwise stability of mild solutions of SPDEs with delays are investigated in this paper. This is achieved by fixed-point methods, so the author makes the following assumptions: Lipschitz conditions on coefficients, exponential estimation of $$C_0$$-semigroup and certain technical condition connecting constants from previous assumptions. These conditions do not require the monotone decreasing behavior of the delays.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35B35 Stability in context of PDEs 93C15 Control/observation systems governed by ordinary differential equations
##### Keywords:
SPDE with delays; mild solution; exponential stability
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##### References:
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