Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 9
113
Views
3
CrossRef citations to date
0
Altmetric
Articles

Analysis of two transmission eigenvalue problems with a coated boundary condition

ORCID Icon
Pages 1996-2019 | Received 29 Apr 2019, Accepted 16 Sep 2019, Published online: 02 Oct 2019

References

  • Cakoni F, Colton D, Haddar H. Inverse scattering theory and transmission eigenvalues. Philadelphia: SIAM Publications; 2016. (CBMS Series; 88).
  • Bondarenko O, Harris I, Kleefeld A. The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary. Appl Anal. 2017;96(1):2–22.
  • Harris I, Kleefeld A. The inverse scattering problem for a conductive boundary condition and transmission eigenvalues. Applicable Analysis. doi:10.1080/00036811.2018.1504028
  • Audibert L, Cakoni F, Haddar H. New sets of eigenvalues in inverse scattering for inhomogeneous media and their determination from scattering data. Inverse Probl. 2017;33:125011.
  • Audibert L, Chesnel L, Haddar H. Transmission eigenvalues with artificial background for explicit material index identification. C R Acad Sci Paris Ser I. 2018;356(6):626–631.
  • Leung Y, Colton D. Complex transmission eigenvalues for spherically stratified media. Inverse Probl. 2012;28:075005.
  • Sun J, Xu L. Computation of Maxwell's transmission eigenvalues and its applications in inverse medium problems. Inverse Probl. 2013;29:104013.
  • Audibert L, Chesnel L, Haddar H. Inside-outside duality with artificial backgrounds, 2019. arXiv:1904.05195.
  • Gintides D, Pallikarakis N. A computational method for the inverse transmission eigenvalue problem. Inverse Probl. 2013;29:104010.
  • Harris I, Cakoni F, Sun J. Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids. Inverse Probl. 2014;30:035016.
  • Kirsch A, Lechleiter A. The inside-outside duality for scattering problems by inhomogeneous media. Inverse Probl. 2013;29:104011.
  • Zeng F, Turner T, Sun J. Some results on electromagnetic transmission eigenvalues. Math Methods Appl Sci. 2015;38(1):155–163.
  • Cakoni F, Haddar H, Harris I. Homogenization of the transmission eigenvalue problem for periodic media and application to the inverse problem. Inverse Probl Imaging. 2015;9(4):1025–1049.
  • Cakoni F, Colton D, Monk P. The linear sampling method in inverse electromagnetic scattering. Philadelphia: SIAM Publications; 2011. (CBMS Series; 80).
  • Bondarenko O, Liu X. The factorization method for inverse obstacle scattering with conductive boundary condition. Inverse Probl. 2013;29:095021.
  • Cakoni F, Haddar H. Identification of partially coated anisotropic buried objects using electromagnetic cauchy data. J Int Eqns Appl. 2007;19(3):361–391.
  • Cakoni F, Haddar H. On the existence of transmission eigenvalues in an inhomogeneous medium. Appl Anal. 2009;88:475–493.
  • Haddar H. The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem. Math Methods Appl Sci. 2004;27(8):2111–2129.
  • Amrouche C, Bernardi C, Dauge M, et al. Vector potentials in three dimensional non-smooth domains. Math Methods Appl Sci. 1998;21(9):823–864.
  • Schweizer B. On Friedrichs Inequality, Helmholtz Decomposition, Vector Potentials, and the div-curl Lemma. Trends in Applications of Mathematics to Mechanics. Switzerland: Springer, 2018. (Springer INdAM Series; 27).
  • Cakoni F, Haddar H. A variational approach for the solution of electromagnetic interior transmission problem for anisotropic media. Inverse Probl Imaging. 2007;1(3):443–456.
  • Kirsch A, Hettlich F. The mathematical theory of time-Harmonic maxwell's equations. New York: Springer; 2015.
  • Evans L. Partial differential equations. Providence: AMS; 2010.
  • An J, Shen J. Spectral approximation to a transmission eigenvalue problem and its applications to an inverse problem. Comp Math with Appl. 2015;69(10):1132–1143.
  • Giovanni G, Haddar H. Computing estimates on material properties from transmission eigenvalues. Inverse Probl. 2012;28:055009.
  • Atkinson K, Han W. Theoretical numerical analysis: a functional analysis framework. 3rd ed. New York: Springer; 2009.
  • Osborn J. Spectral approximation for compact operators. Math Comput. 1975;29:712–725.

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.