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

Jiahui  Zhu; Zdzisław  Brzeźniak

doi:10.3934/dcdsb.2016097

Article Contents

2016, Volume 21, Issue 9: 3269-3299. Doi: 10.3934/dcdsb.2016097

This issue Previous Article Global attractors for $p$-Laplacian differential inclusions in unbounded domains Next Article

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

Jiahui Zhu^1, and
Zdzisław Brzeźniak^2,

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

Received: March 31, 2016

Revised: March 31, 2016

Published: October 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 58J45, 58K30; Secondary: 35L70.

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