This article is cited in 1 paper

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

Yu. F. Dolgii^ab, P. G. Surkov<sup>ba

a</sup> 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.

UDC: 517.929

Received: 31.07.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S55–S67

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