This work is concerned with the homogenization of initial boundary value parabolic equations with hysteresis, containing nonlinear monotone operators in the diffusion term. We make use of the sigma‐convergence concept together with the properties of hysteresis operator to derive the homogenized problem. The homogenized operator is obtained in terms of a solution of a nonlinear corrector problem posed and solved in the usual sense of distributions. We also provide an approximation scheme for the homogenized coefficient.

中文翻译：

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滞后非线性抛物方程的均质化

这项工作涉及具有滞后性的初始边界值抛物方程的均质化，在扩散项中包含非线性单调算子。我们利用sigma-convergence概念以及磁滞算子的性质来推导均化问题。根据在通常的分布意义上提出和解决的非线性校正器问题的解来获得均化算子。我们还提供了均化系数的近似方案。