Détermination du potentiel dans l'équation de Schrödinger à partir de mesures sur une partie du bord

Baudouin, Lucie; Puel, Jean-Pierre

Comptes Rendus. Mathématique, Tome 334 (2002) no. 11, pp. 967-972.

On étudie l'équation de Schrödinger iy′+Δy+qy=0 sur $\Omega \times (0,\mathrm{T})$ avec donnée de Dirichlet $y|\partial \Omega \times (0,T)$ et condition initiale $y|\Omega \times \left\{0\right\}$ et on s'interesse au problème inverse qui consiste à déterminer $\mathrm{q}\left(\mathrm{x}\right),\mathrm{x}\in \Omega$ à partir de la donnée $\frac{\partial y}{\partial \nu }|{\Gamma }_0\times (0,T)$, où Γ₀ est une partie ouverte de $\partial \Omega$ qui vérifie une condition géométrique appropriée. Les détails des démonstrations seront donnés dans [1].

We study the Schrödinger equation iy′+Δy+qy=0 on $\Omega \times (0,\mathrm{T})$ with Dirichlet boundary data $y|\partial \Omega \times (0,T)$ and initial condition $y|\Omega \times \left\{0\right\}$ and we consider the inverse problem of determining the potential q(x), $\mathrm{x}\in \Omega$ when $\frac{\partial y}{\partial \nu }|{\Gamma }_0\times (0,T)$ is given, where Γ₀ is an open subset of $\partial \Omega$ satisfying an appropriate geometrical condition. The detailed proof will be given in [1].

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