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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 10, Pages 3–18 (Mi ivm9039)  

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic solutions of Fredholm integro-differential equations with rapidly changing kernels and irreversible limit operator

A. A. Bobodzhanov, V. F. Safonov

Chair of Higher Mathematics, Moscow Power Engineering Institute, 14 Krasnokazarmennaya str., Moscow, 111250 Russia
Full-text PDF (247 kB) Citations (7)
References:
Abstract: We consider a system of singularly perturbed integro-differential Fredholm equations with rapidly changing kernel in the case of irreversible operator of differential part. We develop an algorithm for constructing regularized asymptotic solutions. It is shown that in the presence of rapidly decreasing multiplier in the kernel the original problem is not on the spectrum (i.e., it is solvable for any right-hand side). We study the limit transition (with small parameter tending to zero), and solve the problem of initialization, i.e., the problem of extracting of the source data for which an exact solution to the system tends to the limit at all duration (including a zone of boundary layer).
Keywords: singular perturbation, boundary layer, integro-differential equation, initialization.
Received: 11.03.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, Volume 59, Issue 10, Pages 1–15
DOI: https://doi.org/10.3103/S1066369X15100011
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: A. A. Bobodzhanov, V. F. Safonov, “Asymptotic solutions of Fredholm integro-differential equations with rapidly changing kernels and irreversible limit operator”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 10, 3–18; Russian Math. (Iz. VUZ), 59:10 (2015), 1–15
Citation in format AMSBIB
\Bibitem{BobSaf15}
\by A.~A.~Bobodzhanov, V.~F.~Safonov
\paper Asymptotic solutions of Fredholm integro-differential equations with rapidly changing kernels and irreversible limit operator
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 10
\pages 3--18
\mathnet{http://mi.mathnet.ru/ivm9039}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 10
\pages 1--15
\crossref{https://doi.org/10.3103/S1066369X15100011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84941992360}
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  • https://www.mathnet.ru/eng/ivm9039
  • https://www.mathnet.ru/eng/ivm/y2015/i10/p3
  • This publication is cited in the following 7 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)
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    Abstract page:238
    Full-text PDF :74
    References:32
    First page:16
     
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