Global Carleman Estimates for Waves and Applications
Global Carleman Estimates for Waves and Applications
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DOI：
10.1080/03605302.2013.771659
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发表时间：
2011-10
影响因子：
1.9
通讯作者：
Lucie Baudouin;Maya de Buhan;S. Ervedoza
中科院分区：
文献类型：
--
作者：
Lucie Baudouin;Maya de Buhan;S. Ervedoza
在这篇文章中，我们广泛地发展了波动方程的Carleman估计，并给出了一些应用。我们专注于观察的情况下的一部分，满足伽玛条件的狮子的边界上的通量。我们将考虑两个应用程序。第一部分讨论了带位势的波动方程的精确能控性问题。根据Fursikov和Imanuvilov在抛物型方程的背景下提出的对偶方法，我们提出了一种建设性的方法来获得控制，弱依赖于潜在的。第二个应用程序涉及的反问题的波，包括在恢复一个未知的时间无关的潜在从一个单一的测量通量。在这种情况下，我们的方法不会产生任何新的稳定性结果，但提出了一个建设性的算法来重建潜力。在这两种情况下，主要思想是引入加权泛函，其中包含Carleman权重，然后利用Carleman参数的自由度来限制势的影响。
In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality method proposed by Fursikov and Imanuvilov in the context of parabolic equations, we propose a constructive method to derive controls that weakly depend on the potentials. The second application concerns an inverse problem for the waves that consists in recovering an unknown time-independent potential from a single measurement of the flux. In that context, our approach does not yield any new stability result, but proposes a constructive algorithm to rebuild the potential. In both cases, the main idea is to introduce weighted functionals that contain the Carleman weights and then to take advantage of the freedom on the Carleman parameters to limit the influences of the potentials.