Date/heure
20 mars 2026
11:00 - 12:00
Oratrice ou orateur
Vesselin Petkov (IMB Bordeaux)
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
We study scattering by obstacles and we consider the scattering kernel $s(t, \theta, \omega)$ which is the Fourier transform of the scattering amplitude. First, we prove the Poisson relation which says that the singularities of scattering kernel with respect to t are included in the set of sojourn times of generalised rays incoming with direction ω and outgoing with direction $\theta$. Second, we establish that for almost all directions $(\omega, \theta)$ the Poisson relation becomes an equality. Thus the sojourn times are observables and they can be considered as scattering data. The situation has similarity with the Poisson relation concerning the singularities of $\sum_j \cos(\lambda_j t)$, where $\lambda^2_j$ are the eigenvalues of the Dirichlet Laplacian $-\Delta$ in bounded domains. We will discuss different inverse scattering problems related to the set of sojourn times. In particular, for a large class of obstacles the knowledge of the sojourn times for almost all directions determines uniquely the form of the obstacle.
The results are obtained in joint works with L. Stoyanov.