Article
MSC:
35B27,
35Q60,
74Q10,
78A25,
78A48,
78M40 | MR 1808428 | Zbl 1058.78004 | DOI: 10.1023/A:1013727504393
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Keywords:
Maxwell’s equations; homogenization; two-scale convergence; corrector results; heterogeneous materials; periodic coefficients; nonperiodic coefficients; compactness result; effective properties; fiber composites
Maxwell’s equations; homogenization; two-scale convergence; corrector results; heterogeneous materials; periodic coefficients; nonperiodic coefficients; compactness result; effective properties; fiber composites
Summary:
The Maxwell equations in a heterogeneous medium are studied. Nguetseng’s method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.
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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: Homogenization and electromagnetic wave propagation in composite media with high conductivity inclusions. In: Proceedings of the Second Workshop Composite Media and Homogenization Theory, G. Dal Maso and G. Dell’Antonio (eds.), World Scientific Publishing Company, Singapore-New York-London, 1995.
[3] M. Artola, M. Cessenat: Un probléme raide avec homogénéisation en électromagnétisme. C. R. Acad. Sci. Paris, Sér. I Math. 310 (1990), 9–14. MR 1044404
[4] M. Artola, M. Cessenat: Diffraction d’une onde électromagnetique par un obstacle borné à permittivité et perméabilité élevées. C. R. Acad. Sci. Paris, Sér. I Math. 314 (1992), 349–354. MR 1153713
[5] A. Bensoussan, J. L. Lions, G. Papanicolaou: Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications. North-Holland Publishing Company, Amsterdam-New York-Oxford, 1978. MR 0503330
[6] M. Cessenat: Mathematical Methods in Electromagnetism. Linear Theory and Applications. Series on Advances in Mathematics for Applied Sciences, Vol 41. World Scientific Publishing Company, Singapore-New York-London, 1996. MR 1409140
[7] G. Duvaut, J. L. Lions: Inequalities in Mechanics and Physics. Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0521262
[8] A. Holmbom: Homogenization of parabolic equations: an alternative approach and some corrector-type results. Appl. Math. 42 (1997), 321–343. DOI 10.1023/A:1023049608047 | MR 1467553 | Zbl 0898.35008
[9] A. Holmbom: The concept of parabolic two-scale convergence, a new compactness result and its application to homogenization of evolution partial differential equations. Research report 1994–18. (1994), Mid-Sweden University, Östersund.
[10] A. Holmbom: Some Modes of Convergence and Their Application to Homogenization and Optimal Composites Design. Ph.D. thesis, Luleå University of Technology, 1996.
[11] P. A. Markowich, F. Poupaud: The Maxwell equation in a periodic medium: Homogenization of the energy density. Ann. Sc. Norm. Sup. Pisa Cl. Sci. 23 (1996), 301–324. MR 1433425
[12] A. Negro: Some problems of homogenization in quasistationary Maxwell equations. In: Applications of Multiple Scaling in Mechanics. Proc. Int. Conf., Ecole Normale Superieure, Paris 1986, Rech. Math. Appl. 4, Masson, Paris, 1987, pp. 246–258. MR 0901998 | Zbl 0644.73077
[13] 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
[14] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44. Springer-Verlag, New York, 1983. MR 0710486
[15] J. Sanchez-Hubert: Étude de certaines équations intégrodifférentielles issues de la théorie de l’homogénéisation. Boll. Un. Mat. Ital. B 5 16 (1979), 857–875. MR 0553802 | Zbl 0421.45009
[16] J. Sanchez-Hubert, E. Sanchez-Palencia: Sur certain problémes physiques d’homogénéisation donnant lieu à des phénomènes de relaxation. C. R. Acad. Sci. Paris, Sér. A 286 (1978), 903–906. MR 0509054
[17] E. Sanchez-Palencia: Non-homogeneous Media and Vibration Theory Lecture Notes in Physics 127. Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 0578345
[18] J. Vanderlinde: Classical Electromagnetic Theory. John Wiley & Sons, New York, 1993.
[19] J. Wyller, N. Wellander, F. Larsson, D. S. Parasnis: Burger’s equation as a model for the IP phenomenon. Geophysical Prospecting 40 (1992), 325–341. DOI 10.1111/j.1365-2478.1992.tb00378.x
[20] E. Zeidler: Nonlinear Functional Analysis and its Applications, Volumes IIA and IIB. Springer-Verlag, Berlin, 1990.
[21] V. V. Zhikov, S. M. Kozlov and O. A. Oleinik: Homogenization of Differential Operators and Integral Functionals. Springer-Verlag, Berlin, 1994. MR 1329546
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