Event
Matthieu Leautaud, Paris & Montr茅al
Monday, November 21, 2016 13:30to14:30
Burnside Hall
Room 920, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Quantitative unique continuation and intensity of waves in the shadow of an obstacle.
The question of global unique continuation is the following: Does the observation of the wave intensity on a little subdomain during a time interval (0,T) determine the total energy of the wave? In an analytic context, this question was solved in 1949 by the well-know Holmgren-John theorem; in the "smooth case", it was finally tackled by Tataru-Robbiano-Zuily-H枚rmander in the nineties. After a review of these results, we shall describe the quantitative unique continuation estimate associated to the qualitative theorem of Tataru-Robbiano-Zuily-H枚rmander, that is, give the optimal logarithmic stability result. In turn, this estimate yields the optimal a priori bound on the penetration of waves into the shadow region, as well as the cost of approximate controls for the wave equation. This is joint work with Camille Laurent. 聽