Two-time-scales hyperbolic-parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles

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• 作者：Bin Pei^a ; ^{xgdsxxpeibin@126.com" class="auth_mail" title="E-mail the corresponding author} ; Yong Xu^a ; ^{hsux3@nwpu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiang-Lun Wu^b ; ^{j.l.wu@swansea.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Averaging principles ; Stochastic hyperbolic&ndash ; parabolic equations ; Poisson random measures ; Two-time-scales
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：243-268
• 全文大小：453 K

文摘

In this article, we are concerned with averaging principle for stochastic hyperbolic–parabolic equations driven by Poisson random measures with slow and fast time-scales. We first establish the existence and uniqueness of weak solutions of the stochastic hyperbolic–parabolic equations. Then, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the stochastic wave equation is an average with respect to the stationary measure of the fast varying process. Finally, we derive the rate of strong convergence for the slow component towards the solution of the averaged equation.