Abstract and Applied Analysis

Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay

Josef Diblík, Denis Khusainov, Oleksandra Kukharenko, and Zdeněk Svoboda

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Abstract

The first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equations of parabolic type with a single delay is possible, an analytical solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 219040, 27 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364846434

Digital Object Identifier
doi:10.1155/2012/219040

Mathematical Reviews number (MathSciNet)
MR2955027

Zentralblatt MATH identifier
1250.35117

Citation

Diblík, Josef; Khusainov, Denis; Kukharenko, Oleksandra; Svoboda, Zdeněk. Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 219040, 27 pages. doi:10.1155/2012/219040. https://projecteuclid.org/euclid.aaa/1364846434


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References

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