How Violent are Fast Controls for Schr�dinger and Plate Vibrations?
نویسندگان
چکیده
منابع مشابه
How Violent Are Fast Controls for Schrödinger and Plate Vibrations
Given a time T > 0 and a region Ω on a compact Riemannian manifold M , we consider the best constant, denoted CT,Ω, in the observation inequality for the Schrödinger evolution group of the Laplacian ∆ with Dirichlet boundary condition: ∀f ∈ L(M), ‖f‖L2(M) ≤ CT,Ω‖e f‖L2((0,T )×Ω). We investigate the influence of the geometry of Ω on the growth of CT,Ω as T tends to 0. By duality, CT,Ω is also th...
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For a linear autonomous system, if a state is reachable from zero in some time duration, then it is reachable within any positive time duration. However, the norm of the control that steers the zero state to the given reachable state will be increasing as the available control time shrinks. This paper gives the asymptotics of minimal L-norm controls as the time duration goes to zero; there are ...
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— In this article, it is shown that the eigenvalues and eigenvector s o f the threedimensional linearized elasticity operator in a thin folded plate converge toward the eigenvalues and eigenvectors of a limit 2d-2d model as the thickness o fthe plates tends to 0. The convergence o f the associated stresses is also established. Resumé. — On montre dans cet article que les valeurs propres et vect...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2004
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-004-0312-y