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Peer-reviewedCC BY 4.0Mathematics

Method of Spectral Mappings for Nonselfadjoint Boundary-Value Problems Associated with Resonance Scattering by Open Structures

  • Garnik V. Abgaryan1
  • Yury V. Shestopalov2
  1. 1Department of Mathematical Simulation, Bauman Moscow State Technical University, 5/1 2nd Baumanskaya St., Moscow 105005, Russia
  2. 2Department of Electronics, Mathematics, and Natural Sciences, Faculty of Engineering and Sustainable Development, University of Gävle, SE 801 76 Gävle, Sweden
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Abstract

We analyze parameter dependence of the complex resonance frequency (RF) spectrum of the nonselfadjoint boundary-value problems associated with a mathematical model of the resonance scattering by an infinite dielectric cylinder. The notions of spectral mapping and spectral set are introduced and applied to solve the addressed problem. A particular focus is toward RF evolution with respect to the varying complex refraction index, visualization of spectral sets, and developing robust methods aimed at the RF calculation and determination of spectral sets.

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Cite

BibTeXRIS
BibTeX
@article{abgaryan2026method,
  title = {{Method of Spectral Mappings for Nonselfadjoint Boundary-Value Problems Associated with Resonance Scattering by Open Structures}},
  author = {Garnik V. Abgaryan and Yury V. Shestopalov},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213850},
  url = {https://www.mdpi.com/2227-7390/14/21/3850},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Method of Spectral Mappings for Nonselfadjoint Boundary-Value Problems Associated with Resonance Scattering by Open Structures
AU  - Garnik V. Abgaryan
AU  - Yury V. Shestopalov
PY  - 2026
DA  - 2026/10/22
JO  - Mathematics
DO  - 10.3390/math14213850
UR  - https://www.mdpi.com/2227-7390/14/21/3850
AB  - We analyze parameter dependence of the complex resonance frequency (RF) spectrum of the nonselfadjoint boundary-value problems associated with a mathematical model of the resonance scattering by an infinite dielectric cylinder. The notions of spectral mapping and spectral set are introduced and applied to solve the addressed problem. A particular focus is toward RF evolution with respect to the varying complex refraction index, visualization of spectral sets, and developing robust methods aimed at the RF calculation and determination of spectral sets.
SN  - 2227-7390
ER  -