Elliptic Carleman Estimates and Applications to Stabilization and Controllability Volume II is popular PDF and ePub book, written by Jérôme Le Rousseau in 2022-04-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Elliptic Carleman Estimates and Applications to Stabilization and Controllability Volume II can be Read Online from any device for your convenience.
Elliptic Carleman Estimates and Applications to Stabilization and Controllability Volume II Book PDF Summary
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.
Detail Book of Elliptic Carleman Estimates and Applications to Stabilization and Controllability Volume II PDF
- Author : Jérôme Le Rousseau
- Release : 22 April 2022
- Publisher : Springer Nature
- ISBN : 9783030886707
- Genre : Mathematics
- Total Page : 542 pages
- Language : English
- PDF File Size : 9,6 Mb
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