Article
MSC:
35B27,
35Q60,
78A25,
78A48 | MR 2059427 | Zbl 1099.35140 | DOI: 10.1023/B:APOM.0000042363.25402.0c
Full entry |
PDF
(2.0 MB)
Feedback
PDF
(2.0 MB)
Feedback
Keywords:
Maxwell equations; homogenization; two-scale convergence; oscillating test functions
Maxwell equations; homogenization; two-scale convergence; oscillating test functions
Summary:
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.
References:
[1] G. Allaire: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992), 1482–2518. DOI 10.1137/0523084 | MR 1185639 | Zbl 0770.35005
[2] M. Artola, M. Cessenat: Sur un problème raide en homogénéisation elliptique. C. R. Acad. Sci., Paris, Sér. I 309 (1989), 761–766. MR 1054959
[3] M. Artola, M. Cessenat: Un problème raide avec homogénéisation en électromagnétisme. C. R. Acad. Sci., Paris, Sér. I 310 (1990), 9–14. MR 1044404
[4] M. Artola, M. Cessenat: Sur la propagation des ondes électromagnétiques dans un milieu composite (diélectrique-conducteur). C. R. Acad. Sci., Paris, Sér. I 310 (1990), 375–380. MR 1046516
[5] M. Artola, M. Cessenat: Problèmes d’homogénéisation diélectrique conducteur dans les composites en structure périodique. Rapport CEA-DAM, Limeil-Valenton, 1990.
[6] A. Bensoussan, J.-L. Lions, and G. Papanicolaou: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam-New York-Oxford, 1978. MR 0503330
[7] A. Bossavit: Electromagnétisme, en vue de la modélisation. Springer-Verlag, Paris, 1991. MR 1616583
[8] M. Bouix: Les discontinuités du rayonnement électromagnétique. Dunod, Paris, 1965. MR 0184544
[9] M. Cessenat: Mathematical Methods in Electromagnetism. Linear Theory and Applications. World Scientific Publishers, River Edge, 1996. MR 1409140 | Zbl 0917.65099
[10] D. Cioranescu, F. Murat: Un terme étrange venu d’ailleurs. In: Nonlinear Partial Differential Equations and Their Applications. Collège de France seminar, Vol. III. Research Notes in Mathematics, H. Brezis, and J. L. Lions (ed.), Pitman, London, 1982, pp. 98–138. MR 0652509
[11] D. Cioranescu, F. Murat: Un terme étrange venu d’ailleurs II. Nonlinear Partial Differential Equations and Their Applications. Coll. de France semin., Vol. II. Research Notes in Mathematics, H. Brezis, J. L. Lions (ed.), Pitman, London, 1982, pp. 154–178. MR 0670272
[12] D. Cioranescu, P. Donato: An Introduction to Homogenization. Oxford Lecture Series in Mathematics and its Applications 17. Oxford University Press, New York-Paris, 1999. MR 1765047
[13] R. Dautray, J. L. Lions: Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol. 2. Masson, Paris, 1985.
[14] G. Nguetseng: A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989), 608–623. DOI 10.1137/0520043 | MR 0990867 | Zbl 0688.35007
[15] J.-S. Hubert, E. Sanchez-Palencia: Introduction aux Méthodes asymptotiques et à l’homogénéisation. Application à la mécaniques des milieux continus. Masson, 1992.
[16] E. Sanchez-Palencia: Non-Homogeneous Media and Vibration Theory. Lectures Notes in Physics 127. Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 0578345
[17] L. Tartar: Cours Peccot. Collège de France, 1977.
[18] L. Tartar: Compensated compactness and applications to partial differential equations. Nonlinear Analysis and Mechanics, Vol. IV, Pitman, Boston-London, 1979, pp. 136–212. MR 0584398 | Zbl 0437.35004
[19] N. Wellander: Homogenization of Maxwell equations, Case I. Linear Theory. Appl. Math. 46 (2001), 29–51. MR 1808428
Search
Partner of
