Moving and oblique observations of beams and plates

Philippe Jaming (1) , Vilmos Komornik (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 IRMA - Institut de Recherche Mathématique Avancée

We study the observability of the one-dimensional Schrödinger equation and of the beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series, we obtain various observability and non-observability theorems. Several open problems are also formulated at the end of the paper.

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Philippe Jaming, Vilmos Komornik. Moving and oblique observations of beams and plates. Evolution Equations & Control Theory, 2020, 9, pp.447-468. ⟨10.3934/eect.2020013⟩. ⟨hal-02068985v2⟩