Partial exact controllability for wave equations

Yong, He

doi:10.1016/j.sysconle.2017.03.001

Cited by 2 publications

(2 citation statements)

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“…We can notice that this condition is written in a slightly different way as Condition 1.1 in [5] and this will be important in the proof of the theorem stated below.…”

Section: Main Results and Relation Between Localized Energy And Localized Controllabilitymentioning

confidence: 99%

“…Concerning Problem 1.4, we recently heard about a very similar work by He [5] on the localized controllability of the wave equation. He gives a geometric condition which is quite similar to ours (but still somewhat different), his strategy of proof is classical and similar to ours but the second part of the proof, namely the strategy leading to the compactness-uniqueness argument is given without any detail in his article.…”

Section: Introductionmentioning

confidence: 99%

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Localization of energy and localized controllability

2021

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We will consider both the controlled Schr\"odinger equation and the controlled wave equation on a bounded open set $\Omega$ of $\RR^{N}$ during an interval of time $(0,T)$, with $T>0$. The control is distributed and acts on a nonempty open subdomain $\omega$ of $\Omega$. On the other hand, we consider another open subdomain $D$ of $\Omega$ and the localized energy of the solution in $D$. The first question we want to study is the possibility of obtaining a prescribed value of this local energy at time $T$ by choosing the control adequately. It turns out that this question is equivalent to a problem of exact or approximate controllability in $D$, which we call localized controllability and which is the second question studied in this article. We obtain sharp results on these two questions and, of course, the answers will require conditions on $\omega$ and $T$ which will be given precisely later on.

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“…We can notice that this condition is written in a slightly different way as Condition 1.1 in [5] and this will be important in the proof of the theorem stated below.…”

Section: Main Results and Relation Between Localized Energy And Localized Controllabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%