Homogenization of the Maxwell equations: Case I. Linear theory

Niklas Wellander

Applications of Mathematics (2001)

  • Volume: 46, Issue: 1, page 29-51
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Wellander, Niklas. "Homogenization of the Maxwell equations: Case I. Linear theory." Applications of Mathematics 46.1 (2001): 29-51. <http://eudml.org/doc/32525>.

@article{Wellander2001,
abstract = {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.},
author = {Wellander, Niklas},
journal = {Applications of Mathematics},
keywords = {Maxwell’s equations; homogenization; two-scale convergence; corrector results; heterogeneous materials; periodic coefficients; nonperiodic coefficients; compactness result; effective properties; fiber composites; homogenization; Maxwell Equations; two-scale convergence; corrector results},
language = {eng},
number = {1},
pages = {29-51},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of the Maxwell equations: Case I. Linear theory},
url = {http://eudml.org/doc/32525},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Wellander, Niklas
TI - Homogenization of the Maxwell equations: Case I. Linear theory
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 1
SP - 29
EP - 51
AB - 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.
LA - eng
KW - Maxwell’s equations; homogenization; two-scale convergence; corrector results; heterogeneous materials; periodic coefficients; nonperiodic coefficients; compactness result; effective properties; fiber composites; homogenization; Maxwell Equations; two-scale convergence; corrector results
UR - http://eudml.org/doc/32525
ER -

References

top
  1. 10.1137/0523084, SIAM J.  Math. Anal. 23 (1992), 1482–2518. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
  2. 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. (1995) 
  3. Un probléme raide avec homogénéisation en électromagnétisme, C.  R.  Acad. Sci. Paris, Sér. I Math. 310 (1990), 9–14. (1990) MR1044404
  4. 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. (1992) MR1153713
  5. Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications, North-Holland Publishing Company, Amsterdam-New York-Oxford, 1978. (1978) MR0503330
  6. 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. (1996) MR1409140
  7. Inequalities in Mechanics and Physics, Springer-Verlag, Berlin-Heidelberg-New York, 1976. (1976) MR0521262
  8. 10.1023/A:1023049608047, Appl. Math. 42 (1997), 321–343. (1997) Zbl0898.35008MR1467553DOI10.1023/A:1023049608047
  9. 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. (1994) 
  10. Some Modes of Convergence and Their Application to Homogenization and Optimal Composites Design, Ph.D.  thesis, Luleå University of Technology, 1996. (1996) 
  11. The Maxwell equation in a periodic medium: Homogenization of the energy density, Ann. Sc. Norm. Sup. Pisa Cl. Sci. 23 (1996), 301–324. (1996) MR1433425
  12. 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. (1987) Zbl0644.73077MR0901998
  13. 10.1137/0520043, SIAM J.  Math. Anal. 20 (1989), 608–623. (1989) Zbl0688.35007MR0990867DOI10.1137/0520043
  14. Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44, Springer-Verlag, New York, 1983. (1983) MR0710486
  15. Étude de certaines équations intégrodifférentielles issues de la théorie de l’homogénéisation, Boll. Un. Mat. Ital. B 5 16 (1979), 857–875. (1979) Zbl0421.45009MR0553802
  16. Sur certain problémes physiques d’homogénéisation donnant lieu à des phénomènes de relaxation, C. R.  Acad. Sci. Paris, Sér. A  286 (1978), 903–906. (1978) MR0509054
  17. Non-homogeneous Media and Vibration Theory Lecture Notes in Physics 127, Springer-Verlag, Berlin-Heidelberg-New York, 1980. (1980) MR0578345
  18. Classical Electromagnetic Theory, John Wiley & Sons, New York, 1993. (1993) 
  19. 10.1111/j.1365-2478.1992.tb00378.x, Geophysical Prospecting 40 (1992), 325–341. (1992) DOI10.1111/j.1365-2478.1992.tb00378.x
  20. Nonlinear Functional Analysis and its Applications, Volumes IIA and IIB, Springer-Verlag, Berlin, 1990. (1990) 
  21. Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. (1994) MR1329546

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.