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Mat. Zametki, 2009, Volume 85, Issue 2, Pages 163–179 (Mi mz4444)  

This article is cited in 3 scientific papers (total in 3 papers)

“Splashes” in Fredholm Integro-Differential Equations with Rapidly Varying Kernels

A. A. Bobodzhanov, V. F. Safonov

Moscow Power Engineering Institute (Technical University)

Abstract: We consider a singularly perturbed Fredholm integro-differential equation with a rapidly varying kernel. We derive an algorithm for constructing regularized asymptotic solutions. It is shown that, given a rapidly decreasing multiplier of the kernel, the original problem does no involve the spectrum (i.e., it is solvable for any right-hand side).

Keywords: integro-differential equation, splash function, Fredholm operator, Volterra operator, regularization of an integral, Lagrange–Sylvester polynomial, boundary layer

DOI: https://doi.org/10.4213/mzm4444

Full text: PDF file (467 kB)
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English version:
Mathematical Notes, 2009, 85:2, 153–167

Bibliographic databases:

UDC: 517.968
Received: 16.11.2007
Revised: 04.06.2008

Citation: A. A. Bobodzhanov, V. F. Safonov, ““Splashes” in Fredholm Integro-Differential Equations with Rapidly Varying Kernels”, Mat. Zametki, 85:2 (2009), 163–179; Math. Notes, 85:2 (2009), 153–167

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bobodzhanova M.A., Safonov V.F., “Asimptoticheskii analiz nelineinykh singulyarno vozmuschennykh integrodifferentsialnykh uravnenii s nulevym operatorom differentsialnoi chasti”, Vestn. Mosk. energeticheskogo in-ta, 2012, no. 6, 30–41  elib
    2. A. A. Bobodzhanov, V. F. Safonov, “The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels”, Sb. Math., 204:7 (2013), 979–1002  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. S. K. Zaripov, “Postroenie analoga teoremy Fredgolma dlya odnogo klassa modelnykh integro-differentsialnykh uravnenii pervogo poryadka s logarifmicheskoi osobennostyu v yadre”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:2 (2017), 236–248  mathnet  crossref  zmath  elib
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