On Weak Observability for Evolution Systems with Skew-Adjoint Generators

Kaïs Ammari (1) , Faouzi Triki (2)

1 FSM - Faculté des Sciences de Monastir
2 EDP - Equations aux Dérivées Partielles

In the paper we consider the linear inverse problem that consists in recovering the initial state in a first order evolution equation generated by a skew-adjoint operator. We studied the well-posedness of the inversion in terms of the observation operator and the spectra of the skew-adjoint generator. The stability estimate of the inversion can also be seen as a weak observability inequality. The proof of the main results is based on a new resolvent inequality and Fourier transform techniques which are of interest themselves.

Domaines: Equations aux dérivées partielles [math.AP]

Kaïs Ammari, Faouzi Triki. On Weak Observability for Evolution Systems with Skew-Adjoint Generators. SIAM Journal on Mathematical Analysis, 2020, 52 (2), pp.1884-1902. ⟨10.1137/19M1241830⟩. ⟨hal-01959822⟩