Abstract:
The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by ‘instability points’ of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems.
Bibliography: 10 titles.
Keywords:
singular perturbation, integro-differential equation, regularizing normal form, asymptotic series.
Citation:
A. A. Bobodzhanov, V. F. Safonov, “The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels”, Sb. Math., 204:7 (2013), 979–1002
\Bibitem{BobSaf13}
\by A.~A.~Bobodzhanov, V.~F.~Safonov
\paper The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels
\jour Sb. Math.
\yr 2013
\vol 204
\issue 7
\pages 979--1002
\mathnet{http://mi.mathnet.ru/eng/sm8139}
\crossref{https://doi.org/10.1070/SM2013v204n07ABEH004327}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3114874}
\zmath{https://zbmath.org/?q=an:06231583}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2013SbMat.204..979B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000324295300003}
\elib{https://elibrary.ru/item.asp?id=20359261}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888377177}
Linking options:
https://www.mathnet.ru/eng/sm8139
https://doi.org/10.1070/SM2013v204n07ABEH004327
https://www.mathnet.ru/eng/sm/v204/i7/p47
This publication is cited in the following 13 articles:
S. K. Zarifzoda, T. K. Yuldashev, “Some Classes of First-Order Integro-Differential Equations and Their Conjugate Equations”, Lobachevskii J Math, 44:7 (2023), 2994
Kalimbetov B.T., Tuychiev O.D., “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
Yuldashev T.K., Zarifzoda S.K., “On a New Class of Singular Integro-Differential Equations”, Bull. Karaganda Univ-Math., 101:1 (2021), 138–148
Yuldashev T.K., Odinaev R.N., Zarifzoda S.K., “On Exact Solutions of a Class of Singular Partial Integro-Differential Equations”, Lobachevskii J. Math., 42:3, SI (2021), 676–684
Bobodzhanov A., Kalimbetov B., Safonov V., “Asymptotic Solutions of Singularly Perturbed Integro-Differential Systems With Rapidly Oscillating Coefficients in the Case of a Simple Spectrum”, AIMS Math., 6:8 (2021), 8835–8853
Yuldashev T.K., Zarifzoda S.K., “New Type Super Singular Integro-Differential Equation and Its Conjugate Equation”, Lobachevskii J. Math., 41:6, SI (2020), 1123–1130
Kalimbetov B.T., Etmishev Kh.F., “Asymptotic Solutions of Scalar Integro-Differential Equations With Partial Derivatives and With Rapidly Oscillating Coefficients”, Bull. Karaganda Univ-Math., 97:1 (2020), 52–67
Kalimbetov B., Safonov V., “Regularization Method For Singularly Perturbed Integro-Differential Equations With Rapidly Oscillating Coefficients and Rapidly Changing Kernels”, Axioms, 9:4 (2020), 131
Kalimbetov B.T., Safonov V.F., “Integro-Differentiated Singularly Perturbed Equations With Fast Oscillating Coefficients”, Bull. Karaganda Univ-Math., 94:2 (2019), 33–47
Bobodzhanov A.A., Kalimbetov B.T., Safonov V.F., “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
S. K. Zaripov, “Postroenie analoga teoremy Fredgolma dlya odnogo klassa modelnykh integrodifferentsialnykh uravnenii pervogo poryadka s singulyarnoi tochkoi v yadre”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 46, 24–35
S. K. Zaripov, “Postroenie analoga teoremy Fredgolma dlya odnogo klassa modelnykh integro-differentsialnykh uravnenii
pervogo poryadka s logarifmicheskoi osobennostyu v yadre”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:2 (2017), 236–248
S. K. Zaripov, “Ob odnoi novoi metodike resheniya odnogo klassa modelnykh integro-differentsialnykh uravnenii pervogo poryadka s singulyarnym yadrom”, Matematicheskaya fizika i kompyuternoe modelirovanie, 20:4 (2017), 68–75
Citation in format AMSBIB
Contact us: