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

Released on by Jérôme Le Rousseau
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  • Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I Book Detail

  • Author : Jérôme Le Rousseau
  • Release Date : 2022-03-28
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 410
  • ISBN 13 : 3030886743
  • File Size : 93,93 MB
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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I by Jérôme Le Rousseau PDF Summary

Book Description: 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 data and associated semigroup, and some elements from functional analysis and semigroup theory.

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Control and Inverse Problems

Control and Inverse Problems

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This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are b