Verfügbarkeit: Control theory for partial differential equations :

Control theory for partial differential equations :: continuous and approximation theories. 1, Abstract parabolic systems /

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Lasiecka, I. (Irena), 1948-
Weitere Verfasser:	Triggiani, R. (Roberto), 1942-
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge ; New York : Cambridge University Press, 2000.
Schriftenreihe:	Encyclopedia of mathematics and its applications ; v. 74.
Schlagworte:	Differential equations, Partial. Control theory. Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS > Differential Equations > Partial. Control theory Differential equations, Partial
Online-Zugang:	Volltext
Beschreibung:	1 online resource : illustrations.
Bibliographie:	Includes bibliographical references and index.
ISBN:	9781107266780 1107266785

Internformat

MARC


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245	1	0	\|a Control theory for partial differential equations : \|b continuous and approximation theories. \|n 1, \|p Abstract parabolic systems / \|c Irena Lasiecka, Roberto Triggiani.
246	3	0	\|a Abstract parabolic systems
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505	8		\|a ""0.4 Abstract Setting for Volume I. The Operator LT in (1.1.9), or LsT in (1.4.1.6), of Chapter 1""""References and Bibliography""; ""1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation""; ""1.1 Mathematical Setting and Formulation of the Problem""; ""1.2 Statement of Main Results""; ""1.2.1 The Nonsmoothing Case. Theorem 1.2.1.1: Existence of a Riccati Operator""; ""1.2.2 Two Smoothing Cases. Theorem 1.2.2.1: Classical Differential Riccati Equation and Uniqueness of the Riccati Operator. Theorem 1.2.2.2""; ""1.3 Orientation""
505	8		\|a ""1.4 Proof of Theorem 1.2.1.1 with GLr Closed""""1.4.1 Optimality. Explicit Representation Formulas for the Optimal Pair {u0, y0}""; ""1.4.2 L2-Estimatesfor {u0,y0} and Zf-Estimate for Gy0(T; . ; x). Limit Relations as s â?? T""; ""1.4.3 Definition of Operators Î? (T, s ) and P(t) and First Properties""; ""1.4.4 Smoothing Properties of Ls and Ls* at t = T, and on Lp(s,T; . )-Spaces. Pointwise Estimates for u0(t, s; x), y0(t, s; x), and P(t)""; ""1.4.5 Smoothing Properties of Ls and Ls* at t = s. Pointwise Regularity of du0(t,s; x)/dt and dy0(t,s; x)/dt for s < t < T, x Îµ Y""
505	8		\|a ""1.7 The Theory of Theorem 1.2.1.1 Is Sharp. Counterexamples When GLÏ? Is Not Closable""""1.7.1 Counterexample to the Existence of the Optimal Control u0 When GLÏ? Is Not Closable""; ""1.7.2 Assumption (1.2.1.26) Is Only Sufficientfor GLÏ? to Be Closed""; ""1.8 Extension to Unbounded Operators R and G""; ""1.8.1 The Case Where R E Â£(1)( (â€?A)Î?); Z) and G E Â£(D((â€?A)Î?); Zf), 0""; ""1A Proof of Lemma 1.5.1.l(iii)""; ""Notes on Chapter 1""
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series	Encyclopedia of mathematics and its applications ;
series2	Encyclopedia of mathematics and its applications ;
spelling	Lasiecka, I. (Irena), 1948- https://id.oclc.org/worldcat/entity/E39PBJrGtXb3pjgm448qPqfXh3 http://id.loc.gov/authorities/names/n87875423 Control theory for partial differential equations : continuous and approximation theories. 1, Abstract parabolic systems / Irena Lasiecka, Roberto Triggiani. Abstract parabolic systems Cambridge ; New York : Cambridge University Press, 2000. 1 online resource : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; 74 Includes bibliographical references and index. Print version record. ""Cover""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""0 Background""; ""0.1 Some Function Spaces Used in Chapter 1""; ""0.2 Regularity of the Variation of Parameter Formula When eAt Is a s.c. Analytic Semigroup""; ""0.2.1 Comments on the Space [X, Y]Â?""; ""0.2.2 Cases Where [D(A),Y]Â? =D((â€?A)Â?)""; ""0.2.3 Comments on the Proof of Proposition 0.1""; ""Properties (0.9), (0.14)""; ""Property (0.10)""; ""Properties (0.11), (0.12)""; ""Properties (0.13)""; ""0.3 The Extrapolation Space [D(A)]'"" ""0.4 Abstract Setting for Volume I. The Operator LT in (1.1.9), or LsT in (1.4.1.6), of Chapter 1""""References and Bibliography""; ""1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation""; ""1.1 Mathematical Setting and Formulation of the Problem""; ""1.2 Statement of Main Results""; ""1.2.1 The Nonsmoothing Case. Theorem 1.2.1.1: Existence of a Riccati Operator""; ""1.2.2 Two Smoothing Cases. Theorem 1.2.2.1: Classical Differential Riccati Equation and Uniqueness of the Riccati Operator. Theorem 1.2.2.2""; ""1.3 Orientation"" ""1.4 Proof of Theorem 1.2.1.1 with GLr Closed""""1.4.1 Optimality. Explicit Representation Formulas for the Optimal Pair {u0, y0}""; ""1.4.2 L2-Estimatesfor {u0,y0} and Zf-Estimate for Gy0(T; . ; x). Limit Relations as s â?? T""; ""1.4.3 Definition of Operators Î? (T, s ) and P(t) and First Properties""; ""1.4.4 Smoothing Properties of Ls and Ls at t = T, and on Lp(s,T; . )-Spaces. Pointwise Estimates for u0(t, s; x), y0(t, s; x), and P(t)""; ""1.4.5 Smoothing Properties of Ls and Ls* at t = s. Pointwise Regularity of du0(t,s; x)/dt and dy0(t,s; x)/dt for s < t < T, x Îµ Y"" ""1.7 The Theory of Theorem 1.2.1.1 Is Sharp. Counterexamples When GLÏ? Is Not Closable""""1.7.1 Counterexample to the Existence of the Optimal Control u0 When GLÏ? Is Not Closable""; ""1.7.2 Assumption (1.2.1.26) Is Only Sufficientfor GLÏ? to Be Closed""; ""1.8 Extension to Unbounded Operators R and G""; ""1.8.1 The Case Where R E Â£(1)( (â€?A)Î?); Z) and G E Â£(D((â€?A)Î?); Zf), 0""; ""1A Proof of Lemma 1.5.1.l(iii)""; ""Notes on Chapter 1"" Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS Differential Equations Partial. bisacsh Control theory fast Differential equations, Partial fast Triggiani, R. (Roberto), 1942- https://id.oclc.org/worldcat/entity/E39PCjGgD4RDR6BDJBYYHmFf9C http://id.loc.gov/authorities/names/n87875424 has work: Control theory for partial differential equations 1 Abstract parabolic systems (Text) https://id.oclc.org/worldcat/entity/E39PCGM6vqV897rXYbwX8x3cGd https://id.oclc.org/worldcat/ontology/hasWork Print version: Lasiecka, I. (Irena), 1948- Control theory for partial differential equations. Cambridge ; New York : Cambridge University Press, 2000 0521434084 (DLC) 99011617 (OCoLC)40682527 Encyclopedia of mathematics and its applications ; v. 74. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589305 Volltext
spellingShingle	Lasiecka, I. (Irena), 1948- Control theory for partial differential equations : continuous and approximation theories. Encyclopedia of mathematics and its applications ; ""Cover""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""0 Background""; ""0.1 Some Function Spaces Used in Chapter 1""; ""0.2 Regularity of the Variation of Parameter Formula When eAt Is a s.c. Analytic Semigroup""; ""0.2.1 Comments on the Space [X, Y]Â?""; ""0.2.2 Cases Where [D(A),Y]Â? =D((â€?A)Â?)""; ""0.2.3 Comments on the Proof of Proposition 0.1""; ""Properties (0.9), (0.14)""; ""Property (0.10)""; ""Properties (0.11), (0.12)""; ""Properties (0.13)""; ""0.3 The Extrapolation Space [D(A)]'"" ""0.4 Abstract Setting for Volume I. The Operator LT in (1.1.9), or LsT in (1.4.1.6), of Chapter 1""""References and Bibliography""; ""1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation""; ""1.1 Mathematical Setting and Formulation of the Problem""; ""1.2 Statement of Main Results""; ""1.2.1 The Nonsmoothing Case. Theorem 1.2.1.1: Existence of a Riccati Operator""; ""1.2.2 Two Smoothing Cases. Theorem 1.2.2.1: Classical Differential Riccati Equation and Uniqueness of the Riccati Operator. Theorem 1.2.2.2""; ""1.3 Orientation"" ""1.4 Proof of Theorem 1.2.1.1 with GLr Closed""""1.4.1 Optimality. Explicit Representation Formulas for the Optimal Pair {u0, y0}""; ""1.4.2 L2-Estimatesfor {u0,y0} and Zf-Estimate for Gy0(T; . ; x). Limit Relations as s â?? T""; ""1.4.3 Definition of Operators Î? (T, s ) and P(t) and First Properties""; ""1.4.4 Smoothing Properties of Ls and Ls at t = T, and on Lp(s,T; . )-Spaces. Pointwise Estimates for u0(t, s; x), y0(t, s; x), and P(t)""; ""1.4.5 Smoothing Properties of Ls and Ls* at t = s. Pointwise Regularity of du0(t,s; x)/dt and dy0(t,s; x)/dt for s < t < T, x Îµ Y"" ""1.7 The Theory of Theorem 1.2.1.1 Is Sharp. Counterexamples When GLÏ? Is Not Closable""""1.7.1 Counterexample to the Existence of the Optimal Control u0 When GLÏ? Is Not Closable""; ""1.7.2 Assumption (1.2.1.26) Is Only Sufficientfor GLÏ? to Be Closed""; ""1.8 Extension to Unbounded Operators R and G""; ""1.8.1 The Case Where R E Â£(1)( (â€?A)Î?); Z) and G E Â£(D((â€?A)Î?); Zf), 0""; ""1A Proof of Lemma 1.5.1.l(iii)""; ""Notes on Chapter 1"" Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS Differential Equations Partial. bisacsh Control theory fast Differential equations, Partial fast
subject_GND	http://id.loc.gov/authorities/subjects/sh85037912 http://id.loc.gov/authorities/subjects/sh85031658
title	Control theory for partial differential equations : continuous and approximation theories.
title_alt	Abstract parabolic systems
title_auth	Control theory for partial differential equations : continuous and approximation theories.
title_exact_search	Control theory for partial differential equations : continuous and approximation theories.
title_full	Control theory for partial differential equations : continuous and approximation theories. 1, Abstract parabolic systems / Irena Lasiecka, Roberto Triggiani.
title_fullStr	Control theory for partial differential equations : continuous and approximation theories. 1, Abstract parabolic systems / Irena Lasiecka, Roberto Triggiani.
title_full_unstemmed	Control theory for partial differential equations : continuous and approximation theories. 1, Abstract parabolic systems / Irena Lasiecka, Roberto Triggiani.
title_short	Control theory for partial differential equations :
title_sort	control theory for partial differential equations continuous and approximation theories abstract parabolic systems
title_sub	continuous and approximation theories.
topic	Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Control theory. http://id.loc.gov/authorities/subjects/sh85031658 Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS Differential Equations Partial. bisacsh Control theory fast Differential equations, Partial fast
topic_facet	Differential equations, Partial. Control theory. Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS Differential Equations Partial. Control theory Differential equations, Partial
url	https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589305
work_keys_str_mv	AT lasieckai controltheoryforpartialdifferentialequationscontinuousandapproximationtheories1 AT triggianir controltheoryforpartialdifferentialequationscontinuousandapproximationtheories1 AT lasieckai abstractparabolicsystems AT triggianir abstractparabolicsystems

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