Abstract We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized equations are stochastic Hamilton-Jacobi equations with deterministic, spatially homogenous Hamiltonians driven by white noise in time. The paper also contains proofs of some general regularity and path stability results for stochastic Hamilton-Jacobi equations, which are needed to prove some of the homogenization results and are of independent interest.

中文翻译：

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混合 Hamilton-Jacobi 方程的标度限制和均匀化

摘要 我们研究了具有高度振荡混合时空依赖性的非线性一阶方程的均匀化。在各种设置中表明，齐次化方程是随机的 Hamilton-Jacobi 方程，具有由时间白噪声驱动的确定性、空间齐次的哈密顿量。该论文还包含对随机 Hamilton-Jacobi 方程的一些一般规律性和路径稳定性结果的证明，这些证明是证明一些同质化结果所必需的，并且具有独立意义。