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Unique continuation property near a corner and its fluid-structure controllability consequences. (English) Zbl 1176.35042

Authors’ abstract: We study a non standard unique continuation property for the biharmonic spectral problem \(\Delta^2\omega=-\lambda\Delta\omega\) 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 \(0<\theta_0<2\pi\), \(\theta_0\neq\pi\) and \(\theta_0\neq 3\pi/2\), 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 side of a corner in a domain containing a Stokes fluids.

MSC:

35B60 Continuation and prolongation of solutions to PDEs
35Q93 PDEs in connection with control and optimization
93B05 Controllability
35P05 General topics in linear spectral theory for PDEs
35J40 Boundary value problems for higher-order elliptic equations
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