论文标题
关于Bresse和Timoshenko系统具有双曲热传导的稳定性
On the stability of Bresse and Timoshenko systems with hyperbolic heat conduction
论文作者
论文摘要
我们研究了三个具有双曲热传导的热弹性光束系统的稳定性。首先，我们研究了Bresse-Gurtin-Pipkin系统，在违反条件时，为指数稳定性和最佳多项式衰减率提供了必要和充分的条件。其次，我们获得了Bresse-Maxwell-Cattaneo系统的类似结果，完成了最近在文献中启动的分析。最后，我们考虑了Timoshenko-gurtin-Pipkin系统，当已知的指数稳定性条件不存在时，我们发现最佳多项式衰减速率。作为副产品，我们充分恢复了Timoshenko-Maxwell-Cattaneo系统的稳定性表征。经典的“相等波速”条件也通过单数极限程序恢复。我们的条件与系数的某些物理限制兼容，因为该系数的积极性是材料比率的阳性。该分析面临着与热阻尼有关的几个挑战，其分辨率取决于最近开发的数学工具，例如定量的riemann-lebesgue引理。
We investigate the stability of three thermoelastic beam systems with hyperbolic heat conduction. First, we study the Bresse-Gurtin-Pipkin system, providing a necessary and sufficient condition for the exponential stability and the optimal polynomial decay rate when the condition is violated. Second, we obtain analogous results for the Bresse-Maxwell-Cattaneo system, completing an analysis recently initiated in the literature. Finally, we consider the Timoshenko-Gurtin-Pipkin system and we find the optimal polynomial decay rate when the known exponential stability condition does not hold. As a byproduct, we fully recover the stability characterization of the Timoshenko-Maxwell-Cattaneo system. The classical "equal wave speeds" conditions are also recovered through singular limit procedures. Our conditions are compatible with some physical constraints on the coefficients as the positivity of the Poisson's ratio of the material. The analysis faces several challenges connected with the thermal damping, whose resolution rests on recently developed mathematical tools such as quantitative Riemann-Lebesgue lemmas.
