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

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 ÍØ-2081.2014.1 This work was supported in part by the Presidential Grant Council (project NSh-2081.2014.1).

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

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English version:
Mathematical Notes, 2017, 102:1, 22–30

Bibliographic databases:

UDC: 517.538

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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• http://mi.mathnet.ru/eng/mz11220
• 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
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
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
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
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