On an extension of the method of two-scale convergence and its applications
On an extension of the method of two-scale convergence and its applications
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论二尺度收敛方法的推广及其应用
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
V. Zhikov
中科院分区：
文献类型：
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作者：
V. Zhikov
引入了固定周期Borel测度的双尺度收敛概念。在这种情况下，得到了环面上的勒贝格测度在Nguetseng-Allaire意义上的收敛性。通过同时考虑函数序列及其梯度序列，揭示了双尺度收敛的主要性质。介绍了双尺度收敛在多孔介质理论（双孔模型）中一些问题均质化问题中的应用。提出了软耦合或弱耦合并行流的数学概念。构造了一个均质算子，并将收敛结果本身解释为一个强双尺度解性收敛。关于谱在均匀化条件下的行为的问题，在这方面被触及。
The concept of two-scale convergence associated with a fixed periodic Borel measure is introduced. In the case when is Lebesgue measure on the torus convergence in the sense of Nguetseng-Allaire is obtained. The main properties of two-scale convergence are revealed by the simultaneous consideration of a sequence of functions and a sequence of their gradients. An application of two-scale convergence to the homogenization of some problems in the theory of porous media (the double-porosity model) is presented. A mathematical notion of softly or weakly coupled parallel flows is worked out. A homogenized operator is constructed and the convergence result itself is interpreted as a strong two-scale resolvent convergence. Problems concerning the behaviour of the spectrum under homogenization are touched upon in this connection.