Solving the Linear 1D Thermoelasticity Equations with Pure Delay

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2015
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Khusainov, Denys Ya
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We propose a system of partial differential equations with a single constant delay r>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1 . 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 r--> 0. Finally, we deduce an explicit solution representation for the delay problem.

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510 Mathematik
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ISO 690KHUSAINOV, Denys Ya, Michael POKOJOVY, 2015. Solving the Linear 1D Thermoelasticity Equations with Pure Delay. In: International Journal of Mathematics and Mathematical Sciences. 2015, 2015, 479267. ISSN 0161-1712. eISSN 1687-0425. Available under: doi: 10.1155/2015/479267
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@article{Khusainov2015Solvi-31401,
  year={2015},
  doi={10.1155/2015/479267},
  title={Solving the Linear 1D Thermoelasticity Equations with Pure Delay},
  volume={2015},
  issn={0161-1712},
  journal={International Journal of Mathematics and Mathematical Sciences},
  author={Khusainov, Denys Ya and Pokojovy, Michael},
  note={Article Number: 479267}
}
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