Determination of singular time-dependent coefficients for wave equations from full and partial data

Abstract : We study the problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $T>0$ and $\Omega$ a $ \mathcal C^2$ bounded domain of $\mathbb R^n$, $n\geq2$. We start by considering the unique determination of some singular time-dependent coefficients from observations on $\partial Q$. Then, by weakening the singularities of the set of admissible coefficients, we manage to reduce the set of data that still guaranties unique recovery of such a coefficient. To our best knowledge, this paper is the first claiming unique determination of unbounded time-dependent coefficients, which is motivated by the problem of determining general nonlinear terms appearing in nonlinear wave equations.
Type de document :
Article dans une revue
Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2018, 12 (3), pp.745-772
Liste complète des métadonnées

Littérature citée [48 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01544811
Contributeur : Yavar Kian <>
Soumis le : jeudi 22 juin 2017 - 10:52:01
Dernière modification le : lundi 9 avril 2018 - 11:13:46
Document(s) archivé(s) le : samedi 16 décembre 2017 - 07:10:20

Fichier

unbounded5.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01544811, version 1

Collections

Citation

Guanghui Hu, Yavar Kian. Determination of singular time-dependent coefficients for wave equations from full and partial data. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2018, 12 (3), pp.745-772. 〈hal-01544811〉

Partager

Métriques

Consultations de la notice

208

Téléchargements de fichiers

38