QUANTITATIVE RAPID AND FINITE TIME STABILIZATION OF THE HEAT EQUATION - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

QUANTITATIVE RAPID AND FINITE TIME STABILIZATION OF THE HEAT EQUATION

Shengquan Xiang
  • Fonction : Auteur
  • PersonId : 1085447

Résumé

The null controllability of the heat equation is known for decades [21, 25, 34]. The finite time stabilizability of the one dimensional heat equation was proved by Coron-Nguyên [15], while the same question for high dimensional spaces remained widely open. Inspired by Coron-Trélat [16] we find explicit stationary feedback laws that quantitatively exponentially stabilize the heat equation with decay rate λ and exp(C\sqrt{λ}) estimates, where Lebeau-Robbiano's spectral inequality [34] is naturally used. Then a piecewise controlling argument leads to null controllability with optimal cost C exp(C/T), as well as finite time stabilization.
Fichier principal
Vignette du fichier
rapheat.pdf (363.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03053731 , version 1 (11-12-2020)

Identifiants

  • HAL Id : hal-03053731 , version 1

Citer

Shengquan Xiang. QUANTITATIVE RAPID AND FINITE TIME STABILIZATION OF THE HEAT EQUATION. 2020. ⟨hal-03053731⟩
387 Consultations
168 Téléchargements

Partager

Gmail Facebook X LinkedIn More