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Solving the Linear 1D Thermoelasticity Equations with Pure Delay

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  • Denys Ya. Khusainov
  • Michael Pokojovy

Abstract

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.

Suggested Citation

  • Denys Ya. Khusainov & Michael Pokojovy, 2015. "Solving the Linear 1D Thermoelasticity Equations with Pure Delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-11, February.
    • Handle: RePEc:hin:jijmms:479267
    DOI: 10.1155/2015/479267
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    Cited by:

    1. Caraballo, Tomás & Cortés, J.-C. & Navarro-Quiles, A., 2019. "Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 198-218.
    2. Juan Carlos Cortés & Marc Jornet, 2020. "L p -Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term," Mathematics, MDPI, vol. 8(6), pages 1-16, June.

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