Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 8
96
Views
6
CrossRef citations to date
0
Altmetric
Articles

Existence and uniqueness theorems in electromagnetic diffraction on systems of lossless dielectrics and perfectly conducting screens

&
Pages 1326-1341 | Received 21 Apr 2016, Accepted 06 May 2016, Published online: 23 May 2016

References

  • Ilynsky AS, Kravtsov VV, Sveshnikov AG. Mathematical models in electromagnetics. Moscow: Vysshaya Shkola; 1991. Russian.
  • Nedelec J-C. Acoustic and electromagnetic equations. integral representations for harmonic problmes. New York (NY): Springer; 2001.
  • Costabel M, Le Louer F. On the Kleinman--Martin integral equation method for electromagnetic scattering by a dielectric body. SIAM J. Appl. Math. 2011;71:635–656.
  • Colton DL, Kress R. integral equation methods in scattering theory. New York (NY): Wiley; 1983.
  • Colton DL, Kress R. Inverse acoustic and electromagnetic scattering theory. Berlin: Springer-Verlag; 1992.
  • Cakoni F, Colton D. A uniqueness theorem for an inverse electromagnetic scattering problem in inhomogeneous anisotropic media. Proc. Edinburgh Math. Soc. 2003;46:293–314.
  • Okaji T. Strong unique continuation property for time harmonic maxwell equations. J. Math. Soc. Jpn. 2002;54:89–122.
  • Samokhin AB. Integral equations and iteration methods in electromagnetic scattering. Utrecht: De Gruyter; 2001.
  • Samokhin AB, editor. Volume integral equation method in problems of mathematical physics. Kyushu: Kyushu University; 2008.
  • Samokhin AB. Volume singular integral equations for problems of scattering on three-dimensional dielectric structures. Differ. Equ. 2014;50:1201–1216.
  • Costabel M, Darrigrand E, Kone EH. Volume and surface integral equations for electromagnetic scattering by a dielectric body. J. Comput. Appl. Math. 2010;234:1817–1825.
  • Kirsch A. An integral eqution approach and the interior transmission problem for maxwell’s equations. Inverse Prob. Imaging. 2007;1:107–127.
  • Protter MH. Unique continuation for elliptic equations. Trans. Amer. Math. Soc. 1960;95:81–91.
  • Ilinsky AS, Smirnov YuG. Electromagnetic wave diffraction by conducting screens. Utrecht: VSP; 1998.
  • Kobayashi K, Shestopalov YuV, Smirnov YuG. Investigation of electromagnetic diffraction by a dielectric body in a waveguide using the method of volume singular integral equation. SIAM J. Appl. Math. 2009;70:969–983.
  • Valovik DV, Smirnov YuG. Pseudodifferential operator method in a problem of the diffraction of an electromagnetic wave on a dielectric body. Differ. Equ. 2012;48:517–523.
  • Smirnov YuG, Tsupak AA. Integrodifferential equations of the vector problem of electromagnetic wave diffraction by a system of nonintersecting screens and inhomogeneous bodies. Adv. Math. Phys. 2015;2015:1–6.
  • Smirnov YuG, Tsupak AA, Valovik DV. On the volume singular integro-differential equation approach for the electromagnetic diffraction problem. Appl. Anal. 2015:1–6. http://www.tandfonline.com/doi/full/10.1080/00036811.2015.1115839
  • Medvedik MYu, Smirnov YuG, Tsupak AA. Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies. Comput. Math. Math. Phys. 2014;54:1280–1292.
  • Smirnov YuG, Tsupak AA. Method of integral equations in the scalar problem of diffraction on a system consisting of a soft and a hard screen and an inhomogeneous body. Differ. Equ. 2014;50:1150–1160.
  • Smirnov YuG, Tsupak AA. Method of integral equations in a scalar diffraction problem on a partially screened inhomogeneous body. Differ. Equ. 2015;51:1225–1235.
  • Ladyzhenskaya OA, Ural’tseva NN. Linear and quasilinear elliptic equations. Moscow: Nauka; 1964. Russian.
  • Lions JL, Magenes E. Non-homogeneous boundary value problems and applications. Vol. 181, Grundlehren der mathematischen Wissenschaften. Berlin: Springer-Verlag; 1972.
  • Rempel S, Schulze B-W. Index theory of elliptic boundary problems. Berlin: Akademie-Verlag; 1982.
  • Stratton JA. Electromagnetic theory. New York (NY): McGraw-Hill Book Company; 1941.
  • Vladimirov VS. Equations of mathematical physics. New York (NY): Marcel Dekker; 1971.
  • Buffa A, Costabel M, Sheen D. On traces for h(curlω) in lipschitz domains. J. Math. Anal. Appl. 2002;276:845–867.
  • Taylor ME. Pseudodifferential operators. Princeton (NJ): Princeton University Press; 1981.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.