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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.

60H15Stochastic partial differential equations
35B35Stability of solutions of PDE
93C15Control systems governed by ODE
Full Text: DOI
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