Journals / Fundamentals of Contemporary Mathematical Sciences / 2026 / Volume: 2 Issue: 1

Asymptotics of Eigenvalues of the Matrix Diffusion Operators

Abdullah Ergün(CUMHURİYET ÜNİVERSİTESİ, SİVAS MESLEK YÜKSEKOKULU)0000-0002-2795-8097
Pages
—
Publication Date
2021-01-29
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Under these conditions, the asymptotic of the eigenvalues of the matrix diffusion operator is obtained, while the Rouche theorem and the Gaussian elimination method are used.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, matrix diffusion equations with boundary conditions and jump conditions on $\left[0,\pi \right]\backslash \left\{a\right\}$ are considered.
📊
Key Findings & Data:In this paper, matrix diffusion equations with boundary conditions and jump conditions on $\left[0,\pi \right]\backslash \left\{a\right\}$ are considered.
💡
Conclusion & Impact:Under these conditions, the asymptotic of the eigenvalues of the matrix diffusion operator is obtained, while the Rouche theorem and the Gaussian elimination method are used.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Matrix diffusion operator · Eigenvalue asymptotics · Spectral data.

Abstract

In this paper, matrix diffusion equations with boundary conditions and jump conditions on $\left[0,\pi \right]\backslash \left\{a\right\}$ are considered. Under these conditions, the asymptotic of the eigenvalues of the matrix diffusion operator is obtained, while the Rouche theorem and the Gaussian elimination method are used.

🔖

Cite This Article

Ergün, A. (2021). Asymptotics of Eigenvalues of the Matrix Diffusion Operators. Fundamentals of Contemporary Mathematical Sciences, Volume: 2 Issue: 1. https://ajindex.com/articles/1486324

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. Titchmarsh E.C., The Theory of Functions, Oxford University Press, 1932.
  2. Papanicolaou V.G., Trace formulas and the behaviour of large eigenvalues, SIAM Journal on Mathematical Analysis, 26(1), 218-237, 1995.
  3. Levitan B.M., Inverse Sturm-Liouville Problems, De Gruyter, 1987.
  4. Carlson R., Large eigenvalues and trace formulas for matrix Sturm-Liouville problems, SIAM Journal on Mathematical Analysis, 30(5), 949-962, 1999.
  5. Shen C.L., Shieh C., On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equations and some related spectral problems, Proceedings of the American Mathematical Society, 127, 2943-2952, 1999.
  6. Beals R., Henkin G.M., Novikova N.N., The inverse boundary problem for the Rayleigh system, Journal of Mathematical Physics, 36(12), 6688-6708, 1995.
  7. Boutet de Monvel A., Shepelsky D., Inverse scattering problem for anisotropic media, Journal of Mathematical Physics, 36(7), 3443-3453, 1995.
  8. Chabanov V.M., Recovering the M-channel Sturm-Liouville operator from M + 1 spectra, Journal of Mathematical Physics, 45(11), 4255-4260, 2004.
  9. Harmer M., Inverse scattering on matrices with boundary conditions, Journal of Physics A: Mathematical and Theoretical, 38(22), 4875-4885, 2005.
  10. Yurko V.A., Inverse spectral problems for differential operators on spatial networks, Russian Mathematical Surveys, 71(3), 539-584, 2016.
  11. Amirov R.K., Nabiev A.A., Inverse problems for the quadratic pencil of the Sturm-Liouville equations with impulse, Abstract and Applied Analysis, Article ID 361989, 2013.