Abstract:
In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved.
Keywords:
singularly perturbed, partial integro differential equation, regularization of an integral, solvability of iterative problems.
Citation:
B. T. Kalimbetov, N. A. Pardaeva, L. D. Sharipova, “Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel”, Sib. Èlektron. Mat. Izv., 16 (2019), 1623–1632
\Bibitem{KalParSha19}
\by B.~T.~Kalimbetov, N.~A.~Pardaeva, L.~D.~Sharipova
\paper Asymptotic solutions of integro-differential equations with partial derivatives and with rapidly varying kernel
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1623--1632
\mathnet{http://mi.mathnet.ru/semr1155}
\crossref{https://doi.org/10.33048/semi.2019.16.113}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000496755800002}
Linking options:
https://www.mathnet.ru/eng/semr1155
https://www.mathnet.ru/eng/semr/v16/p1623
This publication is cited in the following 5 articles:
Musabek AKYLBAYEV, Burhan KALİMBETOV, Nilufar PARDAEVA, “Influence of rapidly oscillating inhomogeneities in the formation of additional boundary layers for singularly perturbed integro-differential systems”, Advances in the Theory of Nonlinear Analysis and its Application, 2023
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
Burkhan Kalimbetov, Valery Safonov, “Singularly Perturbed Integro-Differential Equations With Rapidly Oscillating Coefficients and With Rapidly Changing Kernel in the Case of a Multiple Spectrum”, WSEAS TRANSACTIONS ON MATHEMATICS, 20 (2021), 84
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
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
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