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On the Uniqueness of a Solution to Anisotropic Maxwell’s Equations

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Topics in Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 203))

Abstract

In the present paper we consider Maxwell’s equations in an anisotropic media, when the dielectric permittivity e and the magnetic permeability μ are 3×3 matrices. We formulate relevant boundary value problems, investigate a fundamental solution and find a Silver-Müller type radiation condition at infinity which ensures the uniqueness of solutions when permittivity and permeability matrices are real-valued, symmetric, positive definite and proportional ε = κμ, κ < 0.

The investigation was supported by the grant of the Georgian National Science Foundation GNSF/ST07/3-175.

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Author information

Authors and Affiliations

  1. Andrea Razmadze Mathematical Institute, 1, M. Alexidze str., Tbilisi, 0193, Georgia

    R. Duduchava & D. Kapanadze

  2. Department of Mathematics, Georgian Technical University, 77 M. Kostava st., Tbilisi, 0175, Georgia

    D. Natroshvili

Authors
  1. T. Buchukuri
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  2. R. Duduchava
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  3. D. Kapanadze
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  4. D. Natroshvili
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. Department of Mathematics, College of William and Mary, P. O. Box 8795, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov , Leiba Rodman  & Ilya M. Spitkovsky ,  & 

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112

    J. William Helton

Additional information

Dedicated to Israel Gohberg, the outstanding teacher and scientist, on his 80th birthday anniversary

Communicated by J.A. Ball.

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Buchukuri, T., Duduchava, R., Kapanadze, D., Natroshvili, D. (2010). On the Uniqueness of a Solution to Anisotropic Maxwell’s Equations. In: Ball, J.A., Bolotnikov, V., Rodman, L., Spitkovsky, I.M., Helton, J.W. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 203. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0161-0_6

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