# American Institute of Mathematical Sciences

November  2016, 21(9): 3269-3299. doi: 10.3934/dcdsb.2016097

## Nonlinear stochastic partial differential equations of hyperbolic type driven by Lévy-type noises

 1 School of Science, Zhejiang University of Technology, No. 288, Liuhe Road, Xihu District, Hangzhou 310023, China 2 Department of Mathematics, University of York, Heslington Road, York YO10 5DD

Received  April 2016 Revised  April 2016 Published  October 2016

We study a class of abstract nonlinear stochastic equations of hyperbolic type driven by jump noises, which covers both beam equations with nonlocal, nonlinear terms and nonlinear wave equations. We derive an Itô formula for the local mild solution which plays an important role in the proof of our main results. Under appropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.
Citation: Jiahui Zhu, Zdzisław Brzeźniak. Nonlinear stochastic partial differential equations of hyperbolic type driven by Lévy-type noises. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3269-3299. doi: 10.3934/dcdsb.2016097
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