Exact observability properties of subelliptic wave and Schrödinger equations

Cyril Letrouit (1, 2, 3)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 CaGE - Control And GEometry

In this survey paper, we report on recent works concerning exact observability (and, by duality, exact controllability) properties of subelliptic wave and Schrödinger-type equations. These results illustrate the slowdown of propagation in directions transverse to the horizontal distribution. The proofs combine sub-Riemannian geometry, semi-classical analysis, spectral theory and non-commutative harmonic analysis.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Théorie spectrale [math.SP]

Cyril Letrouit. Exact observability properties of subelliptic wave and Schrödinger equations. 2021. ⟨hal-03109787v2⟩