论文标题
关于弹性和热弹性系统耦合系统的指数稳定性的评论
Remarks on Exponential Stability for a Coupled System of Elasticity and Thermoelasticity with Second Sound
论文作者
论文摘要
我们研究了一个空间维度的线性传输问题解决方案的较大时间行为。手头的问题模拟了由纯粹弹性限制的热弹性材料。我们将表征所考虑系统的所有平衡状态，并证明每个解决方案都在随着时间的时间流向无穷大的一个指定均衡状态。迄今为止，我们采用了强烈连续半群的理论中的方法。特别是，我们为基础发生器获得均匀的分解界限。这消除了[Y.P. Meng和Y.G.王，肛门。应用。 （Singap。）13（2015）]在问题仅具有微不足道的平衡时具有指数衰减率。在附录中，我们为使用傅立叶定律对热传导建模的情况提供了类似的指数稳定性结果。
We study the large time behavior of solutions to a linear transmission problem in one space dimension. The problem at hand models a thermoelastic material with second sound confined by a purely elastic one. We shall characterize all equilibrium states of the considered system and prove that every solution approaches one designated equilibrium state with an exponential rate as time goes to infinity. Hereto, we apply methods from the theory of strongly continuous semigroups. In particular, we obtain uniform resolvent bounds for the underlying generator. This removes the largeness assumption of elastic wave speeds imposed in [Y.P. Meng and Y.G. Wang, Anal. Appl. (Singap.) 13 (2015)] for having an exponential energy decay rate when the problem only has the trivial equilibrium. In an appendix we provide a similar exponential stability result for the case where heat conduction is modeled using Fourier's law.
