Lectures on unique continuation for waves - Sorbonne Université Access content directly
Preprints, Working Papers, ... Year : 2023

Lectures on unique continuation for waves

Camille Laurent
Matthieu Léautaud
  • Function : Author
  • PersonId : 1148857


These notes are intended as an introduction to the question of unique continuation for the wave operator, and some of its applications. The general question is whether a solution to a wave equation in a domain, vanishing on a subdomain has to vanish everywhere. We state and prove two of the main results in the field. We first give a proof of the classical local Hörmander theorem in this context which holds under a pseudoconvexity condition. We then specialize to the case of wave operators with time-independent coefficients and prove the Tataru theorem: local unique continuation holds across any non-characteristic hypersurface. This local result implies a global unique continuation statement which can be interpreted as a converse to finite propagation speed. We finally give an application to approximate controllability, and present without proofs the associated quantitative estimates.
Fichier principal
Vignette du fichier
UC-waves-CIRM-course.pdf (764.51 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04151529 , version 1 (05-07-2023)



Camille Laurent, Matthieu Léautaud. Lectures on unique continuation for waves. 2023. ⟨hal-04151529⟩
6 View
85 Download



Gmail Mastodon Facebook X LinkedIn More