Araştırma Makalesi
BibTex RIS Kaynak Göster

Asymptotics of Eigenvalues of the Matrix Diffusion Operators

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

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.

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

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

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