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Mat. Zametki, 2017, Volume 102, Issue 1, Pages 28–38 (Mi mz11220)  

This article is cited in 4 scientific papers (total in 4 papers)

Regularized Asymptotic Solutions of the Initial Problem for the System of Integro-Partial Differential Equations

A. A. Bobodzhanov, V. F. Safonov

National Research University "Moscow Power Engineering Institute"

Abstract: The Lomov regularization method [1] is generalized to integro-partial differential equations. It turns out that the regularization procedure essentially depends on the type of integral operator. The case in which the upper limit of the integral is not the differentiation variable is the most difficult one. It is not considered in the present paper. Only the case in which the upper limit of the integral operator coincides with the differentiation variable is studied. For such problems, an algorithm for constructing regularized asymptotics is developed.

Keywords: singularly perturbed equation, integro-partial differential equation, regularization of an integral.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-2081.2014.1
This work was supported in part by the Presidential Grant Council (project NSh-2081.2014.1).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11220

Full text: PDF file (460 kB)
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English version:
Mathematical Notes, 2017, 102:1, 22–30

Bibliographic databases:

UDC: 517.538
Received: 04.05.2016

Citation: A. A. Bobodzhanov, V. F. Safonov, “Regularized Asymptotic Solutions of the Initial Problem for the System of Integro-Partial Differential Equations”, Mat. Zametki, 102:1 (2017), 28–38; Math. Notes, 102:1 (2017), 22–30

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11220
  • http://mi.mathnet.ru/eng/mz/v102/i1/p28

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Bobodzhanov, V. F. Safonov, “Regularized asymptotics of solutions to integro-differential partial differential equations with rapidly varying kernels”, Ufa Math. J., 10:2 (2018), 3–13  mathnet  crossref  isi
    2. Yuldashev T.K., “On Inverse Boundary Value Problem For a Fredholm Integro-Differential Equation With Degenerate Kernel and Spectral Parameter”, Lobachevskii J. Math., 40:2 (2019), 230–239  crossref  isi
    3. T. K. Yuldashev, “Spektralnye osobennosti resheniya odnoi kraevoi zadachi dlya integro-differentsialnogo uravneniya Fredgolma vtorogo poryadka s otrazheniem argumenta”, Izv. IMI UdGU, 54 (2019), 122–134  mathnet  crossref  elib
    4. B. T. Kalimbetov, N. A. Pardaeva, L. D. Sharipova, “Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel”, Sib. elektron. matem. izv., 16 (2019), 1623–1632  mathnet  crossref
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