Averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection

Huijie Qiao

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arXiv · 2609.11002

Averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection

Huijie Qiao

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Abstract

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.

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Huijie Qiao. 2026-09-10. Averaging principles for nonautonomous multiscale stochastic Burgers equations with reflection. https://arxiv.org/abs/2609.11002

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