Some uniqueness and observability problems arising in the control of vibrations

Enrique Zuazua

Displaying similar documents to “Some uniqueness and observability problems arising in the control of vibrations”

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The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

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The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input $\to$ state” map in $L_{2}$ -norms is established. A structure of the reachable sets for arbitrary $T > 0$ is studied. In general case, only the first component $u (\cdot, T)$ of the complete state ${u (\cdot, T), u_{t} (\cdot, T)}$ may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data...

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The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing...