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Vincent Laheurte: High-frequency observability cost of hyperbolic systems in several space dimensions


The IAC seminar 2022 on Partial Derivate Equations

Vincent Laheurte (Paris Saclay & Institut de Mathématiques de Bordeaux) will be guest of a PDE IAC seminar.

The event will be held at via dei Taurini 19, seminar room 116, first floor, and will be broadcast in streaming on YouTube IAC channel CNR IAC.

Abstract: The aim of this talk is to present a new method to provide a quantitative study of the high-frequency cost of observability of (linear, but with variable coefficients) hyperbolic systems in several space dimensions. The approach relies on the use of a Fourier multiplier corresponding to the Gramian of the ODE symbolic system that is obtained passing to the Fourier formulation of the hyperbolic PDE, for a given observation operator. A (recorded) energy estimate is obtained by including the multiplier (the Gramian) as a weight inside the Wigner transform of the unknown vector field. The high-frequency observability inequality is achieved by means of the semiclassical Weyl pseudo-differential calculus and related tools. Some examples of applications include the linearized (incompressible and compressible) Euler equations, the Rossby-Poincaré system and partially dissipative hyperbolic systems satisfying the Shizuta-Kawashima condition. This is a joint work with Roberta Bianchini (IAC, CNR) and Franck Sueur (IMB, Bordeaux).