El Akri, AbdeladimManiar, Lahcen2022-02-142022-02-142018-06-27El Akri, A., & Maniar, L. (2018). Indirect boundary observability of semi-discrete coupled wave equations. <i>Electronic Journal of Differential Equations, 2018</i>(133), pp. 1-27.1072-6691https://hdl.handle.net/10877/15333This 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.Text27 pages1 file (.pdf)enAttribution 4.0 InternationalCoupled wave equationsIndirect boundary observabilitySpace semi-discretizationFinite differencesFiltered spacesArticle