Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 7, Pages 62–76 (Mi ivm8811)  
This article is cited in 22 scientific papers (total in 22 papers)

The Dirichlet problem for a loaded mixed-type equation in a rectangular domain

K. B. Sabitov, E. P. Melisheva

Chair of Mathematics and Teaching Principles, Samara State Academy of Social Sciences and Humanities, 26 Antonova-Ovseenko str., Samara, 443090 Russia
Full-text PDF (243 kB) Citations (22)
References:
PDF
HTML
Abstract: We establish necessary and sufficient conditions for the unique solvability of the first boundary problem for a loaded equation with the Lavrent'ev–Bitsadze operator in a rectangular domain. We obtain a solution to the stated problem as the sum of the eigenfunction series for the corresponding one-dimensional problem with respect to eigenvalues. We prove the stability of the solution with respect to boundary functions.
Keywords: loaded mixed-type equation, Dirichlet problem, spectral method, uniqueness, existence, stability.
Received: 16.04.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 7, Pages 53–65
DOI: https://doi.org/10.3103/S1066369X13070062
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, E. P. Melisheva, “The Dirichlet problem for a loaded mixed-type equation in a rectangular domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 7, 62–76; Russian Math. (Iz. VUZ), 57:7 (2013), 53–65
Citation in format AMSBIB
\Bibitem{SabMel13}
\by K.~B.~Sabitov, E.~P.~Melisheva
\paper The Dirichlet problem for a~loaded mixed-type equation in a~rectangular domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 7
\pages 62--76
\mathnet{http://mi.mathnet.ru/ivm8811}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 7
\pages 53--65
\crossref{https://doi.org/10.3103/S1066369X13070062}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84879752682}
Linking options:
  • https://www.mathnet.ru/eng/ivm8811
  • https://www.mathnet.ru/eng/ivm/y2013/i7/p62
    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Statistics & downloads:
    Abstract page:444
    Full-text PDF :190
    References:64
    First page:28
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024