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Matematicheskie Zametki, 2009, Volume 85, Issue 2, Pages 163–179
DOI: https://doi.org/10.4213/mzm4444 (Mi mzm4444) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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

A. A. Bobodzhanov, V. F. Safonov

Moscow Power Engineering Institute (Technical University)
Full-text PDF (467 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm4444
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.
Received: 16.11.2007
Revised: 04.06.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 2, Pages 153–167
DOI: https://doi.org/10.1134/S0001434609010192
Bibliographic databases:
UDC: 517.968
Language: Russian
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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  • https://doi.org/10.4213/mzm4444
  • https://www.mathnet.ru/eng/mzm/v85/i2/p163
    • This publication is cited in the following 7 articles:
    1. Kalimbetov B.T. Etmishev Kh.F., “Asymptotic Solutions of Scalar Integro-Differential Equations With Partial Derivatives and With Rapidly Oscillating Coefficients”, Bull. Karaganda Univ-Math., 97:1 (2020), 52–67  crossref  isi
    2. Kalimbetov B.T., Temirbekov A.N., Yeskarayeva B.I., “Internal Boundary Layer in a Singularly Perturbed Problem of Fractional Derivative”, Bull. Karaganda Univ-Math., 100:4 (2020), 92–100  crossref  isi
    3. Bobodzhanov A.A. Kalimbetov B.T. Safonov V.F., “Singularly Perturbed Control Problems in the Case of the Stability of the Spectrum of the Matrix of An Optimal System”, Bull. Karaganda Univ-Math., 96:4 (2019), 22–38  crossref  isi
    4. Kalimbetov B.T. Safonov V.F., “Integro-Differentiated Singularly Perturbed Equations With Fast Oscillating Coefficients”, Bull. Karaganda Univ-Math., 94:2 (2019), 33–47  crossref  isi
    5. 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
    6. 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
    7. 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
    Citing articles in Google Scholar: Russian citations, English citations
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