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• W2003192057 abstract "In this paper, we shall study the system of transmission of the Schrödinger equation with Dirichlet control and colocated observation. Using the multiplier method, we show that the system is well-posed with input and ouput space<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U equals upper L squared left-parenthesis normal upper Gamma right-parenthesis><mml:semantics><mml:mrow><mml:mi>U</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>L</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>U=L^{2}(Gamma )</mml:annotation></mml:semantics></mml:math></inline-formula>and state space<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X equals upper H Superscript negative 1 Baseline left-parenthesis normal upper Omega right-parenthesis period><mml:semantics><mml:mrow><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>H</mml:mi><mml:mrow class=MJX-TeXAtom-ORD><mml:mo>−<!-- − --></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>.</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>X=H^{-1}(Omega ).</mml:annotation></mml:semantics></mml:math></inline-formula>The regularity of the system is also established, and the feedthrough operator is found to be zero. Finally, the exact controllability of the open-loop system is obtained by proving the observability inequality of the dual system." @default.
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• W2003192057 date "2013-11-13" @default.
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• W2003192057 title "Well-posedness, regularity and exact controllability for the problem of transmission of the Schrödinger equation" @default.
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• W2003192057 doi "https://doi.org/10.1090/s0033-569x-2013-01351-0" @default.
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