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Titlebook: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I; Dirichlet Boundary C Jérôme Le Rousseau,Gilles

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书目名称Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
副标题Dirichlet Boundary C
编辑Jérôme Le Rousseau,Gilles Lebeau,Luc Robbiano
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概述Explores applications of Carleman estimates to study stabilization and controllability properties of PDEs.Covers necessary background material in detail.Complemented by a second volume that considers
丛书名称Progress in Nonlinear Differential Equations and Their Applications
图书封面Titlebook: Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I; Dirichlet Boundary C Jérôme Le Rousseau,Gilles
描述This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation.  All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds..The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter.  Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup.  The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality.  The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet d
出版日期Book 2022
关键词Elliptic Carleman Estimates; Stabilization and Controllability properties of PDEs; Quantified unique c
版次1
doihttps://doi.org/10.1007/978-3-030-88674-5
isbn_softcover978-3-030-88676-9
isbn_ebook978-3-030-88674-5Series ISSN 1421-1750 Series E-ISSN 2374-0280
issn_series 1421-1750
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Giuseppina Albano,Virginia Giorno. 8.4 for references on the precise topology of the various test function and distribution spaces we review here.) adapted to . but we rather define converging sequences in .. First, we define seminorms on ..
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A Short Review of Distribution Theory. 8.4 for references on the precise topology of the various test function and distribution spaces we review here.) adapted to . but we rather define converging sequences in .. First, we define seminorms on ..
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Invariance Under Change of Variablesub-ellipticity property of a differential operator and a weight function (see Definition .). This allows one to freely choose local coordinates for special purposes, as is done in Sect. . for the proof of local Carleman estimates at boundary points.
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https://doi.org/10.1007/978-94-011-5428-4ons. Estimates of this type now bear his name. In the late 50s A.-P. Calderón and L. Hörmander further developed Carleman’s method. To this day, the method based on Carleman estimates remains essential to prove unique continuation properties. In more recent years, the field of applications of Carlem
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Solution of equations: the multigrid methodsay, homogeneous Dirichlet boundary conditions. Here .(.) is a nonnegative bounded function. In the case . ≡ 0 the solution exists for . with an energy that remains constant with respect to .. We shall prove here that if . > 0 on a nonempty open subset . then the energy decays to . as . → +.. The te
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