题目：Observability Inequalities with Compact Remainder
报告人：Guillaume Olive （Jagiellonian University）
In this talk we show that an observability inequality with a compact remainder (equivalently, an observability inequatility on a finite co-dimensional subspace) implies an explicit spectral description of the set of exactly reachable states.
This shows in particular that the compact remainder can be removed if the Fattorini-Hautus test is satisfied.
This result gathers and extends many results of the literature, including the compactness-uniqueness method used for instance in the book of J.L. Lions (1988).
We apply our result to the boundary controllability of many partial differential equations such as that a Schrödinger equation, a beam equation, a Korteweg-de Vries equation, a perturbed wave equation and an integro-differential transport equation.
This talk is based on a joint work with Michel Duprez.
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