No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 28 March 2008
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 $0<\theta_0<2\pi$
,
$\theta_0\not=\pi$
and $\theta_0\not=3\pi/2$
, 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 Izvestiya34 (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.