Boundary sidewise observability of the wave equation

Dehman B, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024


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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.

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Dehman, B., & Zuazua Iriondo, E. (2024). Boundary sidewise observability of the wave equation. (Unpublished, Submitted).


Dehman, Belhassen, and Enrique Zuazua Iriondo. Boundary sidewise observability of the wave equation. Unpublished, Submitted. 2024.

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