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 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 107–118 (Mi timm1004)

Asymptotics of regularized solutions of an ill-posed Cauchy problem for an autonomous linear system of differential equations with commensurable delays

Yu. F. Dolgiiab, P. G. Surkovba

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: For an autonomous linear system of differential equations with commensurable delays, asymptotic formulas are found that describe the analytic dependences of regularized solutions of the system on the regularization parameter. The problem is solved under the requirement that the initial function is sufficiently smooth but with the violation of the conditions that guarantee the continuous extension of solution in the direction of decreasing time.

Keywords: differential equations with delay, ill-posed problem, asymptotic methods.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 287, suppl. 1, 55–67

Bibliographic databases:

Document Type: Article
UDC: 517.929

Citation: Yu. F. Dolgii, P. G. Surkov, “Asymptotics of regularized solutions of an ill-posed Cauchy problem for an autonomous linear system of differential equations with commensurable delays”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 107–118; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 55–67

Citation in format AMSBIB
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This publication is cited in the following articles:
1. P. G. Surkov, “Regulyarizatsiya nekorrektnoi zadachi Koshi dlya avtonomnoi sistemy s zapazdyvaniem pri ispolzovanii odnogo klassa stabilizatorov”, Tr. IMM UrO RAN, 20, no. 3, 2014, 234–245
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