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On Some Homogenization Problems
Author(s) -
Lions J.L.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620503
Subject(s) - homogenization (climate) , ansatz , homogeneous , mathematics , mathematical analysis , mathematical physics , combinatorics , biodiversity , ecology , biology
This expository paper presents some recent results on the “homogenization” process which consists in “approximating” a nonhomogeneous material with a periodic structure by a homogeneous material. Examples of non homogeneous materials are given by composite materials or by performed materials. The approximation is valid when the size ϵ of the period tends to 0. Actually one obtains in some cases higher order terms in the expansion of the state of the system in terms of “powers” of ϵ, with an ansatz of the type of “multiple scale” variables.