Unique continuation property near a corner and its fluid-structure controllability consequences

@article{Osses2009,
abstract = {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.},
author = {Osses, Axel, Puel, Jean-Pierre},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {continuation of solutions of PDE; fluid-structure control; domains with corners; approximate controllability; biharmonic spectral problem; homogeneous Dirichlet boundary conditions; supplementary third order boundary condition},
language = {eng},
number = {2},
pages = {279-294},
publisher = {EDP-Sciences},
title = {Unique continuation property near a corner and its fluid-structure controllability consequences},
url = {http://eudml.org/doc/245115},
volume = {15},
year = {2009},
}

TY - JOUR
AU - Osses, Axel
AU - Puel, Jean-Pierre
TI - Unique continuation property near a corner and its fluid-structure controllability consequences
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2009
PB - EDP-Sciences
VL - 15
IS - 2
SP - 279
EP - 294
AB - 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.
LA - eng
KW - continuation of solutions of PDE; fluid-structure control; domains with corners; approximate controllability; biharmonic spectral problem; homogeneous Dirichlet boundary conditions; supplementary third order boundary condition
UR - http://eudml.org/doc/245115
ER -