Solving the Linear 1D Thermoelasticity Equations with Pure Delay

We propose a systemof partial differential equations with a single constant delay τ > 0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R. 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 τ → 0. Finally, we deduce an explicit solution representation for the delay problem.