Jerome Le Rousseau,Gilles Lebeau,Luc Robbiano
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space
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- More about Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I: Dirichlet Boundary Conditions on Euclidean Space
This monograph discusses Carleman estimates' applications to studying the stabilization and controllability properties of partial differential equations, including the damped wave equation and the heat equation. It derives Carleman estimates using pseudo-differential calculus with a large parameter and addresses continuation issues, proving the logarithmic stabilization of the damped wave equation.
Format: Hardback
Length: 411 pages
Publication date: 29 March 2022
Publisher: Springer Nature Switzerland AG
This monograph delves into the realm of Carleman estimates, exploring their applications in the study of stabilization and controllability properties of partial differential equations. It encompasses various topics, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. The analysis is conducted within the framework of open sets in Euclidean space, with plans to extend this treatment to Riemannian manifolds in a future volume.
The first three chapters provide a comprehensive derivation of Carleman estimates utilizing pseudo-differential calculus with a large parameter. Subsequently, continuation issues are addressed, leading to a proof of the logarithmic stabilization of the damped wave equation through alternative resolvent estimates for the generator of a damped wave semigroup. The authors then delve into the null-controllability of the heat equation, discussing its equivalence with observability, and how the spectral inequality facilitates the construction of control functions or the establishment of observability inequalities.
The final section of the book focuses on presenting essential background material, encompassing the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data, and various elements from functional analysis and semigroup theory. This comprehensive exploration of Carleman estimates and their applications in the study of partial differential equations offers valuable insights to researchers and practitioners in the field.
Weight: 983g
Dimension: 254 x 178 (mm)
ISBN-13: 9783030886738
Edition number: 1st ed. 2022
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