Corrector results for space-time homogenization of nonlinear diffusion
Corrector results for space-time homogenization of nonlinear diffusion
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DOI：
10.2140/memocs.2022.10.171
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发表时间：
2022-01
影响因子：
1.9
通讯作者：
Tomoyuki Oka
中科院分区：
文献类型：
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作者：
Tomoyuki Oka
。本文关注具有周期性振荡（在空间和时间上）系数的非线性扩散方程的时空均匀化问题。主要结果包括梯度、扩散通量和时间导数的校正结果（即，具有校正项的解的强收敛性），而不假设系数的平滑性。主要结果的证明基于时空版本的展开方法，该方法与强二尺度收敛理论密切相关。
. The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of solutions with corrector terms) for gradients, diffusion fluxes and time-derivatives without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.