Solving the Linear 1D Thermoelasticity Equations with Pure Delay

Abstract EN

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 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 τ→0.

Finally, we deduce an explicit solution representation for the delay problem.