Fredholm transformation on Laplacian and rapid stabilization for the heat equations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Fredholm transformation on Laplacian and rapid stabilization for the heat equations

Résumé

We revisit the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient to get controllability and rapid stabilization. This classical framework allows us to present the backstepping method with the Fredholm transformation upon Laplace operators in a sharp functional setting, which is the major objective of this work, from the Riesz basis properties and the operator equality to the stabilizing spaces. Finally, we prove that the same Fredholm transformation also leads to the local rapid stability of the viscous Burgers equation.
Fichier principal
Vignette du fichier
heat.pdf (552.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03319847 , version 1 (13-08-2021)
hal-03319847 , version 2 (08-10-2021)

Identifiants

Citer

Ludovick Gagnon, Amaury Hayat, Shengquan Xiang, Christophe Zhang. Fredholm transformation on Laplacian and rapid stabilization for the heat equations. 2021. ⟨hal-03319847v2⟩
583 Consultations
187 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More