Solving the Linear 1D Thermoelasticity Equations with Pure Delay

We propose a system of partial differential equations with a single constant delay $τ> 0$ 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 $τ\to 0$. Finally, we deduce an explicit solution representation for the delay problem.

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