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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 3, Pages 234–245 (Mi timm1097)  

This article is cited in 1 scientific paper (total in 1 paper)

Regularization of an ill-posed Cauchy problem for an autonomous system with delay with the use of a class of stabilizers

P. G. Surkovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University
Full-text PDF (197 kB) Citations (1)
References:
Abstract: For an autonomous linear system of differential equations with delay, we find asymptotic formulas for the analytic dependence of regularized solutions of this system on a regularization parameter on a finite closed interval of the negative semiaxis. We use the Tychonoff regularization method with a stabilizing functional not generating a compact set in the state space. The problem is solved for sufficiently smooth initial functions, which, however, do not satisfy the conditions that guarantee a continuous extension of solutions to decreasing time.
Keywords: differential equations with delay, ill-posed problem, asymptotic methods.
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: P. G. Surkov, “Regularization of an ill-posed Cauchy problem for an autonomous system with delay with the use of a class of stabilizers”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 234–245
Citation in format AMSBIB
\Bibitem{Sur14}
\by P.~G.~Surkov
\paper Regularization of an ill-posed Cauchy problem for an autonomous system with delay with the use of a~class of stabilizers
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 234--245
\mathnet{http://mi.mathnet.ru/timm1097}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379227}
\elib{https://elibrary.ru/item.asp?id=23503124}
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  • https://www.mathnet.ru/eng/timm/v20/i3/p234
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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