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Asymptotics of Eigenvalues of the Matrix Diffusion Operators

Yıl 2021, Cilt: 2 Sayı: 1, 1 - 7, 29.01.2021

Abdullah Ergün

Öz

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.

Anahtar Kelimeler

Matrix diffusion operator, Eigenvalue asymptotics, Spectral data.

Kaynakça

  • [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.

Yıl 2021, Cilt: 2 Sayı: 1, 1 - 7, 29.01.2021

Abdullah Ergün

Öz

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Articles
Yazarlar

Abdullah Ergün 0000-0002-2795-8097

Yayımlanma Tarihi 29 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 2 Sayı: 1

Kaynak Göster

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.