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
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
MetadataShow full item record
Laboratoire Jean Alexandre Dieudonné [JAD]
Institut Élie Cartan de Lorraine [IECL]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire des Sciences du Numérique de Nantes [LS2N]
Abstract (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.
Subjects / KeywordsDegenerate parabolic equations; backstepping; stabilization; Fredholm transform
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