Well-posedness and exponential stability of a thermoelastic system with internal delay

Résumé

The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction [1]. To avoid this problem, we add to the system, at the delayed equation, a Kelvin–Voigt damping. At first, we prove the well-posedness of the system by the semigroup theory. Next, under appropriate assumptions, we prove the exponential stability of the system by introducing a suitable Lyapunov functional.

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