Abstract
We construct the solving operators of a three-dimensional periodic dielectric waveguide with absorption. The results obtained can be applied to the problem describing a dropping wave onto the interface of two periodic dielectric waveguides with absorption. Bibliography: 6 titles.
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References
V. I. Derguzov and I. V. Denisova, “Projection operators of a three-dimensional periodic waveguide,” Probl. Mat. Anal. [in Russian], 26, 87–138(2003); English transl.: J. Math. Sci., 117, No. 3, (2003)
V. I. Derguzov, “Solution to the ill-posed problem for a class of linear equations with periodic coefficients,” Probl. Mat. Anal. [in Russian], 3, 3–28(1972)
V. I. Derguzov, “The operator Hamiltonians and anticanonical equations with periodic coefficients,” Probl. Mat. Anal. [in Russian], 4, 9–36(1973)
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V. I. Derguzov and I. V. Denisova, “The characteristic spectrum of the reduced wave equation with periodic coefficients in the three-dimensional space,” Probl. Mat. Anal. [in Russian], 21, 110–137(2000); English transl.: J. Math. Sci., 105, No. 5, 2377–2397(2001)
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Denisova, I.V. Resolving Operators for a Three-Dimensional Periodic Waveguide. Journal of Mathematical Sciences 117, 4109–4122 (2003). https://doi.org/10.1023/A:1024808318331
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DOI: https://doi.org/10.1023/A:1024808318331