抽象热弹性延迟系统的适定性与稳定性
Well-posedness and stability of abstract thermoelastic delayed systems
AI总结：
本文研究具有部分耦合延迟的广义热弹性系统，利用半群方法证明其适定性，并通过频域方法建立指数与多项式稳定性，应用于具体实例。
摘要：
本文考虑具有部分耦合延迟的广义热弹性系统（即$α-β$系统）的稳定化问题。针对每种情形，利用半群方法证明相应系统的适定性，随后在充分条件下通过频域方法建立系统指数与多项式稳定性的结果。该结果应用于热弹性中的具体实例。
英文摘要：
In this paper, we consider a stabilization problem of a generalized thermoelastic system (the so called $α-β$ system) with delay in a part of the coupled system. For each case, we prove the well-posedness of the corresponding system using semigroup approach, then under some sufficient conditions we establish some results of exponential and polynomial stability of the system through a frequency-domain approach. The results are applied to concrete examples in thermoelasticity.
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