Abstract

In this article we study the behavior of the solutions for the three-phase-lag heat equation with localized dissipation on an Euler–Bernoulli beam model. We show that semigroup S(t) associated with the problem is of Gevrey class 5 for \(t>0\) . If the coefficients satisfy \(\tau _\alpha > k^{*}\tau _q\) , the solutions are always exponentially stable.

中文翻译：

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局部三相滞后热弹性梁系统的 Gevrey 类

摘要

在本文中，我们研究了欧拉-伯努利梁模型上具有局部耗散的三相滞后热方程的解的行为。我们证明与该问题相关的半群S ( t ) 对于\(t>0\)属于 Gevrey 类 5 。如果系数满足\(\tau _\alpha > k^{*}\tau _q\)，则解始终呈指数稳定。