弱耦合系统的间接边界可观测性

Fatiha Alabau
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引用次数: 26

摘要

本文研究两个波动方程耦合系统的间接边界可观测性。我们表明,在足够长的时间内,如果耦合参数足够小,但不消失,在部分边界上观察解的第一个分量的法向导数的迹迹可以使我们得到初始数据的减弱能量。这个结果引出了一个新的唯一性定理和一个间接的精确可控性结果。
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Observabilité frontière indirecte de systèmes faiblement couplés

This work is concerned with the indirect boundary observability of a coupled system of two wave equations. We show that for a sufficiently large time, the observation of the trace of the normal derivative of the first component of the solution on a part of the boundary allows us to get back a weakened energy of the initial data, this if the coupling parameter is sufficiently small, but non vanishing. This result leads to a new uniqueness theorem and also to an indirect exact controllability result.

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