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Matematicheskie Zametki, 2017, Volume 102, Issue 1, Pages 28–38
DOI: https://doi.org/10.4213/mzm11220
(Mi mzm11220)
 

This article is cited in 14 scientific papers (total in 14 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"
References:
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).
Received: 04.05.2016
English version:
Mathematical Notes, 2017, Volume 102, Issue 1, Pages 22–30
DOI: https://doi.org/10.1134/S0001434617070033
Bibliographic databases:
Document Type: Article
UDC: 517.538
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/mzm11220
  • https://doi.org/10.4213/mzm11220
  • https://www.mathnet.ru/eng/mzm/v102/i1/p28
  • This publication is cited in the following 14 articles:
    1. Tursun Yuldashev, Zhyldyz Artykova, “OB ODNOI ODNORODNOI NELOKALNOI ZADAChE DLYa INTEGRO-DIFFERENTsIALNOGO URAVNENIYa FREDGOLMA VTOROGO PORYaDKA”, VOGUMFT, 2023, no. 1 (2), 239  crossref
    2. Abdukhafiz A. Bobodzhanov, Burkhan T. Kalimbetov, Valeriy F. Safonov, “Algorithm of the regularization method for a singularly perturbed integro-differential equation with a rapidly decreasing kernel and rapidly oscillating inhomogeneity”, Zhurn. SFU. Ser. Matem. i fiz., 15:2 (2022), 216–225  mathnet  crossref  mathscinet
    3. B. T. Kalimbetov, O. D. Tuychiev, “Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity”, Open Math., 19 (2021), 244–258  crossref  mathscinet  isi
    4. B. T. Kalimbetov, Kh. F. Etmishev, “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
    5. B. T. Kalimbetov, A. N. Temirbekov, A. S. Tolep, “Asymptotic solutions of scalar integro-differential equations with partial derivatives and with fast oscillating coefficients”, Eur. J. Pure Appl Math., 13:2 (2020), 287–302  crossref  mathscinet  isi
    6. T. K. Yuldashev, “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  mathscinet  isi  scopus
    7. 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
    8. 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
    9. A. A. Bobodzhanov, B. T. Kalimbetov, V. F. Safonov, “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
    10. T. K. Yuldashev, “Spectral features of the solving of a fredholm homogeneous integro-differential equation with integral conditions and reflecting deviation”, Lobachevskii J. Math., 40:12 (2019), 2116–2123  crossref  mathscinet  zmath  isi
    11. B. T. Kalimbetov, V. F. Safonov, “Integro-differentiated singularly perturbed equations with fast oscillating coefficients”, Bull. Karaganda Univ-Math., 94:2 (2019), 33–47  crossref  isi
    12. T. K. Yuldashev, “On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel”, Comput. Math. Math. Phys., 59:2 (2019), 241–252  mathnet  crossref  crossref  isi  elib
    13. 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
    14. T.K. Yuldashev, “Spectral problem for a Fredholm second-order integro-differential equation”, Dopov. Nac. akad. nauk Ukr., 2018, no. 12, 3  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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