Unique continuation property near a corner and its fluid-structure controllability consequences
ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 2, pp. 279-294.

We study a non standard unique continuation property for the biharmonic spectral problem ${\Delta }^{2}w=-\lambda \Delta w$ in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle $0<{\theta }_{0}<2\pi$, ${\theta }_{0}\ne \pi$ and ${\theta }_{0}\ne 3\pi /2$, a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain containing a Stokes fluid. The proof of the main result is based in a power series expansion of the eigenfunctions near the corner, the resolution of a coupled infinite set of finite dimensional linear systems, and a result of Kozlov, Kondratiev and Mazya, concerning the absence of strong zeros for the biharmonic operator [Math. USSR Izvestiya 34 (1990) 337-353]. We also show how the same methodology used here can be adapted to exclude domains with corners to have a local version of the Schiffer property for the Laplace operator.

DOI: 10.1051/cocv:2008024
Classification: 35B60,  35B37
Keywords: continuation of solutions of PDE, fluid-structure control, domains with corners
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Osses, Axel; Puel, Jean-Pierre. Unique continuation property near a corner and its fluid-structure controllability consequences. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 2, pp. 279-294. doi : 10.1051/cocv:2008024. http://www.numdam.org/articles/10.1051/cocv:2008024/

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