Asymptotic behavior for second order stochastic evolution equations with memory |
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| Authors: | Fei Liang Zhenhua Guo |
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| Institution: | 1. Department of Mathematics, Northwest University, Xi''an, 710069, PR China;2. Department of Mathematics, Xi An University of Science and Technology, Xi''an 710054, PR China |
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| Abstract: | In this paper, a general second order integro-differential evolution equation with memory driven by multiplicative noise is considered. We prove the existence of global mild solution and asymptotic stability of the zero solution using Lyapunov function techniques. Moreover, we discuss three examples to show that the asymptotic stability results can be applied to various partial differential equations. |
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| Keywords: | Stochastic evolution equations Lyapunov functions Exponential stability |
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