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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 479267, 11 pages
Research Article

Solving the Linear 1D Thermoelasticity Equations with Pure Delay

1Department of Cybernetics, Kyiv National Taras Shevchenko University, 64 Volodymyrska Street, Kyiv 01601, Ukraine
2Department of Mathematics and Statistics, University of Konstanz, Universitätsstraße 10, 78457 Konstanz, Germany

Received 27 October 2014; Accepted 3 January 2015

Academic Editor: Harvinder S. Sidhu

Copyright © 2015 Denys Ya. Khusainov and Michael Pokojovy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a system of partial differential equations with a single constant delay describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of . For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as . Finally, we deduce an explicit solution representation for the delay problem.