Abstract and Applied Analysis

On the stability of the linear delay differential and difference equations

A. Ashyralyev and P. E. Sobolevskii

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We consider the initial-value problem for linear delay partial differential equations of the parabolic type. We give a sufficient condition for the stability of the solution of this initial-value problem. We present the stability estimates for the solutions of the first and second order accuracy difference schemes for approximately solving this initial-value problem. We obtain the stability estimates in Hölder norms for the solutions of the initial-value problem of the delay differential and difference equations of the parabolic type.

Article information

Abstr. Appl. Anal., Volume 6, Number 5 (2001), 267-297.

First available in Project Euclid: 13 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65J 65M
Secondary: 47D 34K 34G


Ashyralyev, A.; Sobolevskii, P. E. On the stability of the linear delay differential and difference equations. Abstr. Appl. Anal. 6 (2001), no. 5, 267--297. doi:10.1155/S1085337501000616. https://projecteuclid.org/euclid.aaa/1050266865

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