Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains
Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains
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DOI：
10.1007/978-3-030-35898-3_5
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发表时间：
2018-10
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影响因子：
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通讯作者：
Michela Egidi;Ivica Naki'c;Albrecht Seelmann;Matthias Taufer;Martin Tautenhahn;I. Veselić
中科院分区：
文献类型：
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作者：
Michela Egidi;Ivica Naki'c;Albrecht Seelmann;Matthias Taufer;Martin Tautenhahn;I. Veselić
本文综述了无界区域和有界区域上热方程控制问题的最新研究成果。首先，我们制定新的不确定性关系，分别谱不等式。然后，我们提出了一个抽象的控制成本估计，提高了早期的结果。后者是特别有趣的，当结合前面提到的谱不等式，因为它会产生尖锐的控制成本在几个渐近制度的界限。我们还表明，无界域上的控制问题可以近似为相应的问题上的一系列有界域形成一个用尽。我们的结果也适用于与薛定谔半群相关的广义热方程。
We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost estimate which improves upon earlier results. The latter is particularly interesting when combined with the earlier mentioned spectral inequalities since it yields sharp control cost bounds in several asymptotic regimes. We also show that control problems on unbounded domains can be approximated by corresponding problems on a sequence of bounded domains forming an exhaustion. Our results apply also for the generalized heat equation associated with a Schrödinger semigroup.