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

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- 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 (2008): 279-294. <http://eudml.org/doc/90914>.

@article{Osses2008,

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 $0<\theta_0<2\pi$,
$\theta_0\not=\pi$ 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.
},

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},

month = {3},

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/90914},

volume = {15},

year = {2008},

}

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

DA - 2008/3//

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 $0<\theta_0<2\pi$,
$\theta_0\not=\pi$ 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.

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/90914

ER -

## References

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