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

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 2, page 279-294
- ISSN: 1292-8119

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topOsses, Axel, and Puel, Jean-Pierre. "Unique continuation property near a corner and its fluid-structure controllability consequences." ESAIM: Control, Optimisation and Calculus of Variations 15.2 (2009): 279-294. <http://eudml.org/doc/245115>.

@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 -

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