具有内时滞的热弹性系统的适定性与指数稳定性
Well-posedness and exponential stability of a thermoelastic system with internal delay
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[17]。为了避免这个问题，我们添加到系统中，在延迟方程，Kelvin-Voigt阻尼。首先利用半群理论证明了系统的适定性。其次，在适当的假设下，通过引入适当的李雅普诺夫泛函，证明了系统的指数稳定性。
英文摘要：
The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction [17]. 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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