Exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps |
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Authors: | Zhenting Hou Chenggui Yuan |
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Affiliation: | a School of Mathematics, Central South University, Changsha, Hunan 410075, PR China b Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, UK |
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Abstract: | In this work, we investigate stochastic partial differential equations with variable delays and jumps. We derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions, and generalize the results obtained by Taniguchi [T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl. 331 (2007) 191-205] and Wan and Duan [L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. Probab. Lett. 78 (5) (2008) 490-498] to cover a class of more general stochastic partial differential equations with jumps. Finally, an illustrative example is established to demonstrate our established theory. |
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Keywords: | Stochastic partial differential equation Energy solution Exponential stability Almost sure exponential stability Jumps |
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