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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II

General Boundary Conditions on Riemannian Manifolds de

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Éditeur :

Birkhäuser


Collection :

Progress in Nonlinear Differential Equations and Their Applications

Paru le : 2022-04-22

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Description

This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including quantified unique continuation, logarithmic stabilization of the wave equation, and null-controllability of the heat equation.  Where the first volume derived these estimates in regular open sets in Euclidean space and Dirichlet boundary conditions, here they are extended to Riemannian manifolds and more general boundary conditions.


The book begins with the study of Lopatinskii-Sapiro boundary conditions for the Laplace-Beltrami operator, followed by derivation of Carleman estimates for this operator on Riemannian manifolds.  Applications of Carleman estimates are explored next: quantified unique continuation issues, a proof of the logarithmic stabilization of the boundary-damped wave equation, and a spectral inequality with general boundary conditions to derive the null-controllability result for the heat equation. Two additional chapters consider some more advanced results on Carleman estimates.  The final part of the book is devoted to exposition of some necessary background material: elements of differential and Riemannian geometry, and Sobolev spaces and Laplace problems on Riemannian manifolds.
Pages
547 pages
Collection
Progress in Nonlinear Differential Equations and Their Applications
Parution
2022-04-22
Marque
Birkhäuser
EAN papier
9783030886691
EAN PDF
9783030886707
Informations sur l'ebook
Nombre pages copiables
5
Nombre pages imprimables
54
Taille du fichier
7168 Ko
Prix
168,79 €
EAN EPUB
9783030886707
Informations sur l'ebook
Nombre pages copiables
5
Nombre pages imprimables
54
Taille du fichier
52357 Ko
Prix
168,79 €

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