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Pré-Publication, Document De Travail Année : 2023

Recovering time-dependent singular coefficients of the wave-equation-One Dimensional Case

Olivier Poisson

Résumé

We consider the homogeneous wave equation in the rectangle (0, T )×(0, b), that is, in the one-dimensional space situation. The conductivity depends on the two variables t, x of time and space, and represents an unknown moving inclusion inside the background which has constant conductivity. The waves satisfy the homogeneous Dirichlet condition at x = b and sufficiently smooth but unknown initial conditions at t = 0. We prove that the inclusion is determined by the Dirichlet-to-Neumann mapping defined on the interface x = 0. In fact, we show how the inclusion can be reconstructed from the detection of the singularities of the flux of special waves knowing the singularities of their trace on the interface.
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Dates et versions

hal-02007874 , version 1 (07-02-2019)
hal-02007874 , version 2 (03-10-2023)

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Olivier Poisson. Recovering time-dependent singular coefficients of the wave-equation-One Dimensional Case. 2023. ⟨hal-02007874v2⟩

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