Séminaire POEMS sur les problèmes inverses
14h: Maya De Buhan "RECOVERY OF THE BOTTOM PROFILE 1D TANK CONTAINING A FLUID MODELED BY THE SAINT-VENANT EQUATIONS"
15h30: Sylvain Ervedoza "ON THE RECOVERY OF A POTENTIAL IN A WAVE EQUATION"
The goal of this talk is to present recent works in which we have developed a strategy to recover a potential in a wave equation from one measurement of the flux. We will in particular consider the case in which the potential or the velocity is unknown. Following the setting proposed by Imanuvilov and Yamamoto in a serie of works, I will explain how one can design an algorithm to recover the coefficient of interest, in which in each step one minimizes a strictly convex quadratic functional involving Carleman weights. I will also point out the difficulties arising when adapting this strategy in the numerical setting. I will end up my talk with some numerical simulations. These results are based on joint works with Lucie Baudouin, Maya de Buhan, and Axel Osses.