Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2017

Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach

Résumé

Using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time-varying feedback laws. To this end, on one hand, we provide a new proof of the well-posedness and the ``optimal" bound with respect to damping constants for the solutions of the kernel equations; this allows one to deal with variable coefficients, even with a weak regularity of these coefficients. On another hand, we establish the well-posedness and estimates for the heat equations with a nonlocal boundary condition at one side.
Fichier principal
Vignette du fichier
NullControllability-HeatEquation-2017-02-27.pdf (343.18 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03932302 , version 1 (10-01-2023)

Identifiants

Citer

Jean-Michel Coron, Hoai-Minh Nguyen. Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach. Archive for Rational Mechanics and Analysis, 2017, 225 (3), pp.993-1023. ⟨10.1007/s00205-017-1119-y⟩. ⟨hal-03932302⟩
10 Consultations
72 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More