Propagation of electromagnetic waves in non-homogeneous media

Radjesvarane Alexandre; Hassan Taha

Applications of Mathematics (2004)

  • Volume: 49, Issue: 3, page 201-225
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Alexandre, Radjesvarane, and Taha, Hassan. "Propagation of electromagnetic waves in non-homogeneous media." Applications of Mathematics 49.3 (2004): 201-225. <http://eudml.org/doc/33183>.

@article{Alexandre2004,
abstract = {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.},
author = {Alexandre, Radjesvarane, Taha, Hassan},
journal = {Applications of Mathematics},
keywords = {Maxwell equations; homogenization; two-scale convergence; oscillating test functions; Maxwell equations; homogenization; two-scale convergence; oscillating test functions},
language = {eng},
number = {3},
pages = {201-225},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Propagation of electromagnetic waves in non-homogeneous media},
url = {http://eudml.org/doc/33183},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Alexandre, Radjesvarane
AU - Taha, Hassan
TI - Propagation of electromagnetic waves in non-homogeneous media
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 3
SP - 201
EP - 225
AB - 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.
LA - eng
KW - Maxwell equations; homogenization; two-scale convergence; oscillating test functions; Maxwell equations; homogenization; two-scale convergence; oscillating test functions
UR - http://eudml.org/doc/33183
ER -

References

top
  1. 10.1137/0523084, SIAM J.  Math. Anal. 23 (1992), 1482–2518. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
  2. Sur un problème raide en homogénéisation elliptique, C. R. Acad. Sci., Paris, Sér.  I 309 (1989), 761–766. (1989) MR1054959
  3. Un problème raide avec homogénéisation en électromagnétisme, C. R. Acad. Sci., Paris, Sér.  I 310 (1990), 9–14. (1990) MR1044404
  4. Sur la propagation des ondes électromagnétiques dans un milieu composite (diélectrique-conducteur), C. R. Acad. Sci., Paris, Sér.  I 310 (1990), 375–380. (1990) MR1046516
  5. Problèmes d’homogénéisation diélectrique conducteur dans les composites en structure périodique, Rapport CEA-DAM, Limeil-Valenton, 1990. (1990) 
  6. Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam-New York-Oxford, 1978. (1978) MR0503330
  7. Electromagnétisme, en vue de la modélisation, Springer-Verlag, Paris, 1991. (1991) MR1616583
  8. Les discontinuités du rayonnement électromagnétique, Dunod, Paris, 1965. (1965) MR0184544
  9. Mathematical Methods in Electromagnetism. Linear Theory and Applications, World Scientific Publishers, River Edge, 1996. (1996) Zbl0917.65099MR1409140
  10. 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. (1982) MR0652509
  11. 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. (1982) MR0670272
  12. An Introduction to Homogenization. Oxford Lecture Series in Mathematics and its Applications 17, Oxford University Press, New York-Paris, 1999. (1999) MR1765047
  13. Analyse mathématique et calcul numérique pour les sciences et les techniques, Vol.  2, Masson, Paris, 1985. (1985) 
  14. 10.1137/0520043, SIAM J. Math. Anal. 20 (1989), 608–623. (1989) Zbl0688.35007MR0990867DOI10.1137/0520043
  15. Introduction aux Méthodes asymptotiques et à l’homogénéisation. Application à la mécaniques des milieux continus, Masson, 1992. (1992) 
  16. Non-Homogeneous Media and Vibration Theory. Lectures Notes in Physics  127, Springer-Verlag, Berlin-Heidelberg-New York, 1980. (1980) MR0578345
  17. Cours Peccot, Collège de France, 1977. (1977) 
  18. Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics, Vol. IV, Pitman, Boston-London, 1979, pp. 136–212. (1979) Zbl0437.35004MR0584398
  19. Homogenization of Maxwell equations, Case  I. Linear Theory, Appl. Math. 46 (2001), 29–51. (2001) MR1808428

NotesEmbed ?

top

You must be logged in to post comments.