Applied Mathematics Seminar

Professor Laurent Bourgeois ENSTA, Institut Polytechnique de Paris (France)

In this talk, we address  forward and inverse scattering problems in an infinite Kirchhoff-Love plate, the scatterer being an impenetrable obstacle of any shape.

Four kinds of boundary conditions are considered on the boundary of such obstacle : clamped, simply-supported, roller-supported and free.

Concerning the forward problem, we  prove well-posedness in these four situations, for any  wave number in the first three ones,  except for a countable set of wave numbers in the last case (the free boundary conditions model a hole in the plate), which is the most difficult one.  

We then address the inverse problem of retrieving obstacles from near-field data. In this view, we adapt the Linear Sampling Method of Colton-Kirsch to image the obstacles, showing numerical results to illustrate the feasibility.

The forward part of this work is a collaboration with Christophe Hazard, the inverse part is a collaboration with Arnaud Recoquillay.