Averaging principle for slow-fast stochastic partial differential equations with H\"{o}lder continuous coefficients

TL;DR

This paper establishes an averaging principle for slow-fast stochastic partial differential equations with H"{o}lder continuous coefficients, using Zvonkin's transformation and Khasminskii's discretization, supported by an illustrative example.

Contribution

It introduces a novel approach combining Zvonkin's transformation and Khasminskii's method to handle SPDEs with H"{o}lder continuous drifts, extending existing averaging results.

Findings

Proved averaging principle for a class of SPDEs with H"{o}lder continuous coefficients.

Developed a new analytical framework using Zvonkin's transformation.

Provided an example demonstrating the applicability of the theoretical results.

Abstract

By using the technique of the Zvonkin's transformation and the classical Khasminkii's time discretization method, we prove the averaging principle for slow-fast stochastic partial differential equations with bounded and H\"{o}lder continuous drift coefficients. An example is also provided to explain our result.