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...

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...