On Exponential Instability of an Inverse Problem for the Wave Equation

2025/06/30 by Busch, Leonard, Lassas, Matti, Oksanen, Lauri +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.23559

Abstract

For a time-independent potential q∈ L^∞, consider the source-to-solution operator that maps a source f to the solution u=u(t,x) of (\Box+q)u=f in Euclidean space with an obstacle, where we impose on u vanishing Cauchy data at t=0 and vanishing Dirichlet data at the boundary of the obstacle. We study the inverse problem of recovering the potential q from this source-to-solution map restricted to some measurement domain. By giving an example where measurements take place in some subset and the support of q lies in the `shadow region' of the obstacle, we show that recovery of q is exponentially unstable.

Citations

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Cited by

• Stability of Gel'fand's inverse interior spectral problem for Schrödinger operators

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