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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I - Dirichlet Boundary Conditions on Euclidean Space (Hardcover, 1st ed. 2022)
Loot Price: R4,410
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Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I - Dirichlet Boundary Conditions on Euclidean Space (Hardcover, 1st ed. 2022)
Series: Progress in Nonlinear Differential Equations and Their Applications, 97
Expected to ship within 10 - 15 working days
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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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