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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 1, Pages 46–63 (Mi ivm9536)  

Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation

N. V. Martemyanova

Samara National Research University, 34 Moskovskoye shosse, Samara, 443086 Russia

Abstract: We consider the equation of mixed elliptic-hyperbolic type. Right part of this equation is represented as a product of two functions, each of a single variable. We study an inverse problem for this equation to find unknown multipliers. We establish a criterion of the uniqueness of a solution to this problem. Solution was constructed as a sums of series on the systems of eigenfunctions corresponding one-dimensional spectral problem. We have obtained estimates bounded away from zero for small denominators. The existence and stability is proved under certain conditions upon the ratio of the rectangle sides of hyperbolic part of the equation, upon boundary functions and known multipliers in the right parts of equation.

Keywords: equation of mixed type, inverse problem, spectral method, uniqueness, small denominators, existence, stability.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-31-50018_мол_нр
16-31-00421_мол_а


DOI: https://doi.org/10.26907/0021-3446-2020-1-46-63

Full text: PDF file (421 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 517.95
Received: 20.09.2018
Revised: 21.07.2019
Accepted: 25.09.2019

Citation: N. V. Martemyanova, “Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 1, 46–63

Citation in format AMSBIB
\Bibitem{Mar20}
\by N.~V.~Martemyanova
\paper Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev--Bitsadze equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 1
\pages 46--63
\mathnet{http://mi.mathnet.ru/ivm9536}
\crossref{https://doi.org/10.26907/0021-3446-2020-1-46-63}


Linking options:
  • http://mi.mathnet.ru/eng/ivm9536
  • http://mi.mathnet.ru/eng/ivm/y2020/i1/p46

    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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:72
    References:6
    First page:3

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