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arXiv · 1410.7236

Solving the Linear 1D Thermoelasticity Equations with Pure Delay

Denys Ya. Khusainov·Michael Pokojovy
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Abstract

We propose a system of partial differential equations with a single constant delay $\tau > 0$ describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of $\mathbb{R}^{1}$. For an initial-boundary value problem associated with this system, we prove a global 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 $\tau \to 0$. Finally, we deduce an explicit solution representation for the delay problem.

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Denys Ya. Khusainov, Michael Pokojovy. 2014-10-27. Solving the Linear 1D Thermoelasticity Equations with Pure Delay. https://arxiv.org/abs/1410.7236

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