On some problems of homogenization

Author:
J. M. Burgers

Journal:
Quart. Appl. Math. **35** (1978), 421-434

MSC:
Primary 35A35; Secondary 65P05

DOI:
https://doi.org/10.1090/qam/479821

MathSciNet review:
479821

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Abstract | References | Similar Articles | Additional Information

Abstract: This article concerns a type of partial differential equations in which coefficients occur that are periodic functions of the basic independent variables or coordinates , (we restrict ourselves to two-dimensional problems). The period length , here assumed to be the same in both directions, is supposed to be small in comparison with the scale of the general field, and interest is directed to what happens when . An example is the equation

*constant*coefficients, and how these coefficients can be obtained from the . This is called the problem of

*"homogenization"*.

**[1]**I. Babuška.*Homogenization and its applications; mathematical and computational problems*, in*Numerical solutions of partial differential equations III*, B. Hubbard, ed., Academic Press, 1976**[2]**I. Babuška,*Homogenization approach in engineering*, in*Proc. symposium on computing methods in engineering*, Dec. 15-19, 1945, Versailles, France**[3]**G. Duvaut,*Analyse fonctionelle et mécanique des milieus continus, application à l'etude des matériaux composites elastiques à structure périodique-homogénéisation*, in:*Theoretical and Applied Mechanics*, Preprints IUTAM Congress, W. T. Koiter, ed., Aug. 30-Sept.**4**, 1976, Delft, Netherlands, pp. 110-132**[4]**J. L. Lions, A. Bensoussan, G. Papanicolau, book in preparation**[5]**Ivo Babuška,*Solution of interface problems by homogenization. I*, SIAM J. Math. Anal.**7**(1976), no. 5, 603–634. MR**0509273**, https://doi.org/10.1137/0507048

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DOI:
https://doi.org/10.1090/qam/479821

Article copyright:
© Copyright 1978
American Mathematical Society