非线性扩散时空均匀化的校正结果

IF 1 Q4 MECHANICS Mathematics and Mechanics of Complex Systems Pub Date : 2022-01-19 DOI:10.2140/memocs.2022.10.171

Tomoyuki Oka

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引用次数: 1

摘要

．本文研究具有周期振荡(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。主要结果的证明是基于展开方法的时空版本，这与强双尺度收敛理论密切相关。

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Corrector results for space-time homogenization of nonlinear diffusion

. 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.

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.