Titlebook: Carleman Estimates and Applications to Uniqueness and Control Theory; Ferruccio Colombini,Claude Zuily Book 2001 Springer Science+Business

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Carleman Estimate and Decay Rate of the Local Energy for the Neumann Problem of Elasticity, an arbitrary obstacle with Neumann or Dirichlet boundary conditions are considered. We prove that there exists an exponentially small neighborhood of the real axis free of resonances. Consequently we prove that for regular data, the energy decays at least as fast as the inverse of the logarithm of

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,Observability of the Schr?dinger Equation,s are obtained from different works on the control of the heat equation or of the wave equation. From the theory of exact and approximate controllability,introduced by J.L. Lions [.], we know that observation is equivalent to approximate controllability and stable observation is equivalent to exact

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Some Results and Open Problems on the Controllability of Linear and Semilinear Heat Equations,ains and (b) The linear heat equation in the half line. Concerning the first problem (a) we show that a number of systems in which blow-up arises may be controlled by means of external forces which are localized in an arbitrarily small open set. In the frame of problem (b) we prove that compactly su

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AlxGa1-xAs: dielectric function,t satisfied..Our second result is about exact control for the Schr?dinger equation see 2) and is inspired by a transform introduced by L. Boutet de Monvel [.] for the study of the propagation of singularities of an analogous solution of the Schr?dinger equation. Our strategy is to construct an exact

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,Observability of the Schr?dinger Equation,t satisfied..Our second result is about exact control for the Schr?dinger equation see 2) and is inspired by a transform introduced by L. Boutet de Monvel [.] for the study of the propagation of singularities of an analogous solution of the Schr?dinger equation. Our strategy is to construct an exact