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001445663 001__ 1445663
001445663 003__ OCoLC
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001445663 019__ $$a1306526716$$a1308396591$$a1308798617$$a1309049598
001445663 020__ $$a9783030886745$$q(electronic bk.)
001445663 020__ $$a3030886743$$q(electronic bk.)
001445663 020__ $$z9783030886738$$q(print)
001445663 020__ $$z3030886735$$q(print)
001445663 0247_ $$a10.1007/978-3-030-88674-5$$2doi
001445663 035__ $$aSP(OCoLC)1308975032
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001445663 049__ $$aISEA
001445663 050_4 $$aQA331
001445663 08204 $$a515/.9$$223
001445663 1001_ $$aLe Rousseau, Jérôme,$$eauthor.
001445663 24510 $$aElliptic Carleman estimates and applications to stabilization and controllability.$$nVolume I,$$pDirichlet boundary conditions on Euclidean space /$$cJérôme Le Rousseau, Gilles Lebeau, Luc Robbiano.
001445663 24630 $$aDirichlet boundary conditions on Euclidean space
001445663 264_1 $$aCham, Switzerland :$$bBirkhäuser,$$c2022.
001445663 300__ $$a1 online resource (viii, 411 pages) :$$billustrations (some color).
001445663 336__ $$atext$$btxt$$2rdacontent
001445663 337__ $$acomputer$$bc$$2rdamedia
001445663 338__ $$aonline resource$$bcr$$2rdacarrier
001445663 4901_ $$aProgress in nonlinear differential equations and their applications, PNLDE subseries in control,$$x2731-7374 ;$$vvolume 97
001445663 504__ $$aIncludes bilbiographical references and indexes.
001445663 5050_ $$aIntroduction -- Part 1: Calculus with a Large Parameter, Carleman Estimates Derivation -- (Pseudo-)differential Operators with a Large Parameter -- Carleman Estimate for a Second-Order Elliptic Operator -- Optimality Aspects of Carleman Estimates -- Part 2: Applications of Carleman Estimates -- Unique Continuation -- Stabilization of the Wave Equation with an Inner Damping -- Controllability of Parabolic Equations -- Part 3: Background Material: Analysis and Evolution Equations -- A Short Review of Distribution Theory -- Invariance under Change of Variables -- Elliptic Operator with Dirichlet Data and Associated Semigroup -- Some Elements of Functional Analysis -- Some Elements of Semigroup Theory -- Bibliography -- Subject Index -- Index of Notation.
001445663 506__ $$aAccess limited to authorized users.
001445663 520__ $$aThis monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.
001445663 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 5, 2022).
001445663 650_0 $$aCarleman theorem.
001445663 650_0 $$aDifferential equations, Partial.
001445663 650_6 $$aMéthode de Carleman.
001445663 650_6 $$aÉquations aux dérivées partielles.
001445663 655_0 $$aElectronic books.
001445663 7001_ $$aLebeau, Gilles,$$eauthor.
001445663 7001_ $$aRobbiano, Luc,$$eauthor.
001445663 77608 $$iPrint version:$$aLe Rousseau, Jérôme$$tElliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I$$dCham : Springer International Publishing AG,c2022$$z9783030886738
001445663 830_0 $$aProgress in nonlinear differential equations and their applications.$$pPNLDE Subseries in Control ;$$vv. 97.
001445663 852__ $$bebk
001445663 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88674-5$$zOnline Access$$91397441.1
001445663 909CO $$ooai:library.usi.edu:1445663$$pGLOBAL_SET
001445663 980__ $$aBIB
001445663 980__ $$aEBOOK
001445663 982__ $$aEbook
001445663 983__ $$aOnline
001445663 994__ $$a92$$bISE