Singular perturbations and homogenization in stratified media
Singular perturbations and homogenization in stratified media
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分层介质中的奇异扰动和均质化
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
C. Picard
中科院分区：
文献类型：
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作者：
G. Bouchitté;C. Picard
我们考虑在某一方向(例如x1)上分层的异质结构。假设条带具有很高的导电性，这意味着导电性系数a{x1)在|0.+∞|上振荡，而不需要a和a-1的通常的有界性假设(关于L∞范数)。C.Picard J.Mossino和B.Heron已经考虑过这个问题，他们特别研究了扩散方程作为∊-0的渐近行为：假设序列(a∊)和(a∊)-1对于L1的弱拓扑是极限的。在本文中(另见预印本[19])。当(a∊)和(a∊)1弱收敛于一般的Radon测度，如m和tr时，我们提出了一个新的方法(凸泛函)，它允许我们传递到(*)中的极限.由于矫顽力的损失，解序列(u∊)的极限可能具有不连续性，其能量(与∊的奇性部分有关)集中在与解序列(U)正交的超平面上。
We consider a heterogeneous structure which is stratified in some direction (say x1). The strips are assumed to have very high conductivity which means that the conductivity coefficient a{x1) ranges over |0.+ ∞| oscillating without the usual boundedness assumption (with respect to the L∞-norm) of a and a-1 This problem has been already considered by C.Picard J. Mossino and B.Heron who studied in particular the asymptotic behaviour as ∊-0 of the diffusion equation: boundary condition under the assumption that the sequences (a∊) and (a∊)-1 have limits for the weak topology of L1. In this paper (see also preprint [19]). we propose a new method (convex functionals on measures ranging into L2 which allow us to pass to the limit in (*) when (a∊) and (a∊)1converges ∗-weakly to general Radon measures, say m and tr. Due to the loss of coercivity, the limit of the sequence of solutions (u∊) may have discontinuities whose energy (associated to the singular part of ∊) is concentrated on hyperplanes orthogonal to the ...