An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media

Valery Yakhno; Ali Sevimlican

Applications of Mathematics (2011)

  • Volume: 56, Issue: 3, page 315-339
  • ISSN: 0862-7940

Abstract

top
The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.

How to cite

top

Yakhno, Valery, and Sevimlican, Ali. "An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media." Applications of Mathematics 56.3 (2011): 315-339. <http://eudml.org/doc/116528>.

@article{Yakhno2011,
abstract = {The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.},
author = {Yakhno, Valery, Sevimlican, Ali},
journal = {Applications of Mathematics},
keywords = {equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform; equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform},
language = {eng},
number = {3},
pages = {315-339},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media},
url = {http://eudml.org/doc/116528},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Yakhno, Valery
AU - Sevimlican, Ali
TI - An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 315
EP - 339
AB - The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.
LA - eng
KW - equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform; equations of electromagnetic theory; hyperbolic system of second order partial differential equations; initial value problem; analytical method; Fourier transform
UR - http://eudml.org/doc/116528
ER -

References

top
  1. Andersen, N. D., 10.2140/pjm.2004.213.1, Pac. J. Math. 213 (2004), 1-13. (2004) Zbl1049.43004MR2040247DOI10.2140/pjm.2004.213.1
  2. Apostol, T. M., Calculus I, Blaisdell Publishing Company Waltham, Massachusetts-Toronto-London (1967). (1967) MR0214705
  3. Bang, H. H., 10.1090/S0002-9947-1995-1283539-1, Trans. Am. Math. Soc. 347 (1995), 1067-1080. (1995) Zbl0828.42009MR1283539DOI10.1090/S0002-9947-1995-1283539-1
  4. Burridge, R., Qian, J., 10.1017/S0956792506006486, Eur. J. Appl. Math. 17 (2006), 63-94. (2006) Zbl1160.78001MR2228972DOI10.1017/S0956792506006486
  5. Cohen, G. C., Higher-Order Numerical Methods for Transient Wave Equations, Springer Berlin (2002). (2002) Zbl0985.65096MR1870851
  6. Courant, R., Hilbert, D., Methods of Mathematical Physics, Vol. 2, Interscience Publishers New York-London (1962). (1962) 
  7. Eom, H. J., Electromagnetic Wave Theory for Boundary-Value Problems, Springer Berlin (2004). (2004) Zbl1053.78001MR2081952
  8. Evans, L. C., Partial Differential Equations, AMS Providence (1998). (1998) Zbl0902.35002MR1625845
  9. Gronwall, T. H., 10.2307/1967124, Ann. Math. 20 (1919), 292-296. (1919) MR1502565DOI10.2307/1967124
  10. Krowne, C. M., 10.1080/00207218508920702, Int. J. Electron. 3 (1985), 315-332. (1985) DOI10.1080/00207218508920702
  11. Ludwig, D., 10.1002/cpa.3160140203, Commun. Pure Appl. Math. 14 (1961), 113-124. (1961) Zbl0112.21202MR0127703DOI10.1002/cpa.3160140203
  12. Melrose, R. B., Uhlmann, G. A., 10.1215/S0012-7094-79-04630-1, Duke Math. J. 46 (1979), 571-582. (1979) Zbl0422.58026MR0544247DOI10.1215/S0012-7094-79-04630-1
  13. Ortner, N., Wagner, P., 10.1002/zamm.200310130, ZAMM, Z. Agew. Math. Mech. 84 (2004), 314-346. (2004) MR2057145DOI10.1002/zamm.200310130
  14. Sheen, J., 10.1163/1569393054069082, J. Electromagn. Waves Appl. 19 (2005), 754-767. (2005) MR2191918DOI10.1163/1569393054069082
  15. Tuan, V. K., Zayed, A. I., 10.1006/jmaa.2001.7740, J. Math. Anal. Appl. 266 (2002), 200-226. (2002) Zbl0998.44001MR1876778DOI10.1006/jmaa.2001.7740
  16. Uhlmann, G. A., 10.1002/cpa.3160350104, Commun. Pured Appl. Math. 35 (1982), 69-80. (1982) Zbl0516.35055MR0637495DOI10.1002/cpa.3160350104
  17. Vladimirov, V. S., Equations of Mathematical Physics, Marcel Dekker New York (1971). (1971) Zbl0231.35002MR0268497
  18. Yakhno, V. G., 10.1088/0305-4470/38/10/015, J. Phys. A: Math. Gen. 38 (2005), 2277-2287. (2005) MR2126517DOI10.1088/0305-4470/38/10/015
  19. Yakhno, V. G., Yakhno, T. M., Kasap, M., 10.1016/j.ijsolstr.2005.07.028, Int. J. Solids Struct. 43 (2006), 6261-6276. (2006) MR2265178DOI10.1016/j.ijsolstr.2005.07.028
  20. Yakhno, V. G., 10.1016/j.ijengsci.2007.12.005, Int. J. Eng. Sci. 46 (2008), 411-426. (2008) Zbl1213.78029MR2401286DOI10.1016/j.ijengsci.2007.12.005

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.