Indirect boundary observability of semi-discrete coupled wave equations
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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.
CitationEl Akri, A., & Maniar, L. (2018). Indirect boundary observability of semi-discrete coupled wave equations. Electronic Journal of Differential Equations, 2018(133), pp. 1-27.
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