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.
General
| Imprint: |
Springer Nature Switzerland AG
|
| Country of origin: |
Switzerland |
| Series: |
PNLDE Subseries in Control, 97 |
| Release date: |
March 2023 |
| First published: |
2022 |
| Authors: |
Jérôme Le Rousseau
• Gilles Lebeau
• Luc Robbiano
|
| Dimensions: |
254 x 178mm (L x W) |
| Pages: |
411 |
| Edition: |
1st ed. 2022 |
| ISBN-13: |
978-3-03-088676-9 |
| Categories: |
Books
|
| LSN: |
3-03-088676-X |
| Barcode: |
9783030886769 |
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