Boundary sidewise observability of the wave equation
Dehman B, Zuazua Iriondo E (2025)
Publication Language: English
Publication Status: Accepted
Publication Type: Journal article, Original article
Future Publication Type: Journal article
Publication year: 2025
Journal
Publisher: J. Eur. Math. Soc. (JEMS)
URI: https://dcn.nat.fau.eu/wp-content/uploads/Dehman-Zuazua.pdf
DOI: 10.4171/JEMS/1688
Open Access Link: https://ems.press/journals/jems/articles/14299033
Abstract
The wave equation on a bounded domain of Rn with non homogeneous boundary Dirichlet data or sources supported on a subset of the boundary is considered. We analyze the problem of observing the source out of boundary measurements done away from its support.
We first show that observability inequalities may not hold unless an infinite number of derivatives are lost, due to the existence of solutions that are arbitrarily concentrated near the source.
We then establish observability inequalities in Sobolev norms, under a suitable microlo- cal geometric condition on the support of the source and the measurement set, for sources fulfilling pseudo-differential conditions that exclude these concentration phenomena.
The proof relies on microlocal arguments and is essentially based on the use of microlocal defect measures.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Tunisia (TN)How to cite
APA:
Dehman, B., & Zuazua Iriondo, E. (2025). Boundary sidewise observability of the wave equation. Journal of the European Mathematical Society. https://doi.org/10.4171/JEMS/1688
MLA:
Dehman, Belhassen, and Enrique Zuazua Iriondo. "Boundary sidewise observability of the wave equation." Journal of the European Mathematical Society (2025).
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