Indirect boundary observability of semi-discrete coupled wave equations
| dc.contributor.author | El Akri, Abdeladim | |
| dc.contributor.author | Maniar, Lahcen | |
| dc.date.accessioned | 2022-02-14T21:46:24Z | |
| dc.date.available | 2022-02-14T21:46:24Z | |
| dc.date.issued | 2018-06-27 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 27 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | El 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15333 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Coupled wave equations | |
| dc.subject | Indirect boundary observability | |
| dc.subject | Space semi-discretization | |
| dc.subject | Finite differences | |
| dc.subject | Filtered spaces | |
| dc.title | Indirect boundary observability of semi-discrete coupled wave equations | |
| dc.type | Article |