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Stability criteria of stochastic partial differential equations with variable delays ∗

Abstract. Some criteria for the asymptotic stability of nonlinear stochastic partial differential equations with variable delays are presented. A coercivity condition plays the role of an exponential stability criterion. Consequently, under the coercivity condition almost all the trajectories of the nonstationary solutions of the given stochastic system finally tend exponentially to zero. Two examples are studied to illustrate our theory.