Fredholm transformation on Laplacian and rapid stabilization for the heat equations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

Fredholm transformation on Laplacian and rapid stabilization for the heat equations

Abstract

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
Origin Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

Ludovick Gagnon, Amaury Hayat, Shengquan Xiang, Christophe Zhang. Fredholm transformation on Laplacian and rapid stabilization for the heat equations. 2021. ⟨hal-03319847v2⟩
591 View
192 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More