发表机构
School of Mathematics, Southeast University（东南大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在最小假设下建立带反射的非自治多尺度随机Burgers方程的一般 averaging 原理，通过周期或渐近条件得到两个系数不依赖小参数的独立平均方程，并给出实例验证。
AI 中文摘要
本文研究了带反射的非自治多尺度随机Burgers方程的 averaging 原理。首先，在最小假设下，我们推导了一个适用于此类方程的一般 averaging 原理。随后，由于所得平均方程的系数仍依赖于小尺度参数 $\e$，我们对系数施加周期或渐近条件，从而得到两个系数不依赖于 $\e$ 的不同平均方程，并建立了两个 averaging 原理。停时和 Khasminskii 的时间离散化方案在其中发挥了重要作用。最后，我们提供了一个具体例子来说明理论结果的适用性和有效性。
英文摘要
In this paper, we study averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection. First, we derive a general averaging principle applicable to such equations under minimal assumptions. Subsequently, since the coefficients of the obtained averaged equation still depend on the small scaling parameter $\e$, we impose either periodic or asymptotic conditions on the coefficients, thereby obtain two distinct averaged equations whose coefficients are independent of $\e$ and establish two averaging principles. Stopping times and Khasminskii's time discretization schemes play an important role. Finally, a concrete example is provided to illustrate the applicability and validity of the theoretical results.
Comments39 pages
