This paper deals with the periodic homogenization of nonlocal parabolic Hamilton–Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal operator, giving rise to three different cell problems and effective operators. To prove the locally uniform convergence to the unique solution of the Cauchy problem for the effective equation we need a new comparison principle among viscosity semi-solutions of integrodifferential equations that can be of independent interest.

中文翻译：

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具有矫顽梯度项的非局部 Hamilton-Jacobi 方程的柯西问题和周期性均匀化

本文处理了梯度项中具有超线性增长的非局部抛物线 Hamilton-Jacobi 方程的周期性均匀化。我们表明，该问题根据非本地算子的顺序呈现出不同的特征，从而产生了三种不同的小区问题和有效的算子。为了证明有效方程的柯西问题的唯一解的局部一致收敛，我们需要一个新的积分微分方程粘度半解之间的比较原理，它可以是独立感兴趣的。