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Preprints, Working Papers, ... Year : 2023

Mathematical analysis of an observer for solving inverse source wave problem

Abstract

The objective of this work is to propose a method using observers to estimate a source term of a wave equation from internal measurements in a subdomain. The first part of the work consists in proving an identifiability result from classical observability conditions for wave equations. We show that the source reconstruction is an ill-posed inverse problem of degree 1 or 2 depending on the measurements type. This inverse problem is solved using observers -- a sequential strategy -- that is proven to be equivalent to a minimization of a cost functional with Tikhonov regularization.
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Dates and versions

hal-04344193 , version 1 (14-12-2023)

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  • HAL Id : hal-04344193 , version 1

Cite

Tiphaine Delaunay, Sébastien Imperiale, Philippe Moireau. Mathematical analysis of an observer for solving inverse source wave problem. 2023. ⟨hal-04344193⟩
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