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Sbornik: Mathematics, 2001, Volume 192, Issue 8, Pages 1139–1164
DOI: https://doi.org/10.1070/SM2001v192n08ABEH000586 (Mi sm586) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Volterra integral equations with rapidly varying kernels and their asymptotic integration

A. A. Bobodzhanov, V. F. Safonov

Moscow Power Engineering Institute (Technical University)
English version PDF (241 kB) Citations (23)
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DOI: https://doi.org/10.1070/SM2001v192n08ABEH000586
Abstract: This paper is concerned with a singularly perturbed integral system with rapidly varying kernels. In contrast to integral equations with slowly varying kernels, where regularization is carried out with respect to the spectrum of the “diagonal” kernel, the regularization problem in the case of rapidly varying kernels is solved in terms of the spectrum of a certain extended operator. The goal here is to construct this operator and develop an appropriate algorithm for asymptotic solutions.
Received: 17.11.2000
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 8, Pages 53–78
DOI: https://doi.org/10.4213/sm586
Bibliographic databases:
UDC: 517.968
MSC: Primary 45D05, 45F15; Secondary 34E05, 34E15, 47A52, 47G20
Language: English
Original paper language: Russian
Citation: A. A. Bobodzhanov, V. F. Safonov, “Volterra integral equations with rapidly varying kernels and their asymptotic integration”, Mat. Sb., 192:8 (2001), 53–78; Sb. Math., 192:8 (2001), 1139–1164
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:33
    References:94
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