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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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    • 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
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