ABSTRACT

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.

中文翻译：

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具有内滞的热弹性系统的适定性和指数稳定性

摘要

热弹性系统中延迟的存在破坏了热传导的适定性和稳定效应[1]。为了避免这个问题，我们在延迟方程中向系统添加了 Kelvin-Voigt 阻尼。首先，我们用半群理论证明了系统的适定性。接下来，在适当的假设下，我们通过引入合适的 Lyapunov 泛函来证明系统的指数稳定性。