Abdeladim El Akri, Lahcen Maniar
Abstract:
This work concerns the indirect observability properties for the
finite-difference space semi-discretization of the 1-d coupled wave equations
with homogeneous Dirichlet boundary conditions. We assume that only one of
the two components of the unknown is observed. As for a single wave equation,
as well as for the direct (complete) observability of the coupled wave equations,
we prove the lack of the numerical observability. However, we show that a
uniform observability holds in the subspace of solutions in which the initial
conditions of the observed component is generated by the low frequencies.
Our main proofs use a two-level energy method at the discrete level and a
Fourier decomposition of the solutions.
Submitted September 17, 2017. Published June 27, 2018.
Math Subject Classifications: 65M06.
Key Words: Coupled wave equations; indirect boundary observability;
space semi-discretization; finite differences; filtered spaces.
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Abdeladim El Akri Cadi Ayyad University Faculty of Sciences Semlalia LMDP, UMMISCO (IRD-UPMC) BP. 2390, Marrakesh, Morocco email: ekr.abdeladim@gmail.com |
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Lahcen Maniar Cadi Ayyad University Faculty of Sciences Semlalia LMDP, UMMISCO (IRD-UPMC) BP. 2390, Marrakesh, Morocco email: maniar@uca.ma |
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