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arXiv · 1810.11229

Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains

Michela Egidi·Ivica Nakić·Albrecht Seelmann·Matthias Täufer·Martin Tautenhahn·Ivan Veselic
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Abstract

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. It 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 Schr\"odinger semigroup.

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Michela Egidi, Ivica Nakić, Albrecht Seelmann, Matthias Täufer, Martin Tautenhahn, Ivan Veselic. 2018-10-26. Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains. https://arxiv.org/abs/1810.11229

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