论文标题
多项式生长的一类非自治慢快速系统的强大平均原理
Strong averaging principles for a class of non-autonomous slow-fast systems of SPDEs with polynomial growth
论文作者
论文摘要
在这项工作中，我们研究了由泊松随机测量驱动的一类非自治的两次随机反应扩散方程，其中系数满足多项式生长条件和局部Lipschitz条件。首先，通过构建辅助方程并使用停止时间的技术来证明温和解决方案的存在和独特性。然后，考虑到系数的时间，平均方程是通过研究与冻结快速方程相关的时间依赖性进化家族的存在来重新定义的。此外，通过使用经典的khasminskii方法验证了慢速分量强烈收敛到相应平均方程的解。
In this work, we study a class of non-autonomous two-time-scale stochastic reaction-diffusion equations driven by Poisson random measures, in which the coefficients satisfy the polynomial growth condition and local Lipschitz condition. First, the existence and uniqueness of the mild solution are proved by constructing auxiliary equations and using the technique of stopping time. Then, consider that the time dependent of the coefficients, the averaged equation is redefined by studying the existence of time-dependent evolution family of measures associated with the frozen fast equation. Further, the slow component strongly converges to the solution of the corresponding averaged equation is verified by using the classical Khasminskii method.
