Nonlinear Stochastic Partial Differential Equations of hyperbolic type driven by Lévy-type noises
Nonlinear Stochastic Partial Differential Equations of hyperbolic type driven by Lévy-type noises
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DOI：
10.3934/dcdsb.2016097
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发表时间：
2016-10
影响因子：
1.2
通讯作者：
Jiahui Zhu;Z. Brzeźniak
中科院分区：
文献类型：
--
作者：
Jiahui Zhu;Z. Brzeźniak
研究了一类由跳跃噪声驱动的抽象非线性双曲型随机方程，它既包括具有非局部非线性项的梁方程，也包括非线性波动方程。我们推导出一个伊藤公式的局部温和的解决方案，发挥了重要作用，我们的主要结果的证明。在适当的条件下，证明了该问题的解的非爆炸性和渐近稳定性。
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 Ito 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.