RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 2, Pages 274–284 (Mi timm1429)  

Perturbation of a waveguide by a narrow potential

I. Kh. Khusnullin

Bashkir State Pedagogical University, Ufa

Abstract: We study a boundary value problem in a band with Fourier boundary condition. The problem models a waveguide perturbed by a narrow complex potential of large intensity. The potential depends on a small parameter and a large parameter. The small parameter corresponds to the diameter of the support of the potential, and the large parameter corresponds to the maximum value of the potential. The product of the parameters tends to zero. The problem corresponds to mathematical models of a quantum waveguide and an acoustic waveguide. In this statement, in contrast to the statements considered earlier, a weaker constraint is imposed on the ratio of the parameters and the Fourier conditions are given at the boundary of the band. The main content of this paper is the construction of a special transform that takes the original operator to an operator with a small localized perturbation; the transform preserves the spectrum of the operator. We obtain a condition on the potential under which an eigenvalue appears from the edge of the continuous spectrum; in this case, we find the leading terms of the asymptotics of the eigenvalue. We also obtain a condition for the absence of such an eigenvalue. The results are formulated in a theorem.

Keywords: perturbation, waveguide, eigenvalue.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00066 мол-а)
Grant of the Republic of Bashkortostan 4


DOI: https://doi.org/10.21538/0134-4889-2017-23-2-274-284

Full text: PDF file (201 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.928.1
MSC: 34E10, 76M45, 81Q15
Received: 01.08.2016

Citation: I. Kh. Khusnullin, “Perturbation of a waveguide by a narrow potential”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 274–284

Citation in format AMSBIB
\Bibitem{Khu17}
\by I.~Kh.~Khusnullin
\paper Perturbation of a waveguide by a narrow potential
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 2
\pages 274--284
\mathnet{http://mi.mathnet.ru/timm1429}
\crossref{https://doi.org/10.21538/0134-4889-2017-23-2-274-284}
\elib{https://elibrary.ru/item.asp?id=29295270}


Linking options:
  • http://mi.mathnet.ru/eng/timm1429
  • http://mi.mathnet.ru/eng/timm/v23/i2/p274

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:113
    Full text:15
    References:19
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020