
A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation
Gagnon, Ludovick; Lissy, Pierre; Marx, Swann (2021), A Fredholm transformation for the rapid stabilization of a degenerate parabolic equation, SIAM Journal on Control and Optimization, 59, 5, p. 3828–3859. 10.1137/20M1372603
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Type
Article accepté pour publication ou publiéDate
2021Nom de la revue
SIAM Journal on Control and OptimizationVolume
59Numéro
5Éditeur
SIAM - Society for Industrial and Applied Mathematics
Pages
3828–3859
Identifiant publication
Métadonnées
Afficher la notice complèteAuteur(s)
Gagnon, LudovickLaboratoire Jean Alexandre Dieudonné [LJAD]
Institut Élie Cartan de Lorraine [IECL]
Lissy, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Marx, Swann

Laboratoire des Sciences du Numérique de Nantes [LS2N]
Résumé (EN)
This paper deals with the rapid stabilization of a degenerate parabolic equation with a right Dirich-let control. Our strategy consists in applying a backstepping strategy, which seeks to find an invertible transformation mapping the degenerate parabolic equation to stabilize into an exponentially stable system whose decay rate is known and as large as we desire. The transformation under consideration in this paper is Fredholm. It involves a kernel solving itself another PDE, at least formally. The main goal of the paper is to prove that the Fredholm transformation is well-defined, continuous and invertible in the natural energy space. It allows us to deduce the rapid stabilization.Mots-clés
Degenerate parabolic equations; backstepping; stabilization; Fredholm transformPublications associées
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