Control theory for partial differential equations :: continuous and approximation theories. 2, Abstract hyperbolic-like systems over a finite time horizon /
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2000.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 75. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (xxi, pages 645-1067, [5] pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107089013 1107089018 |
Internformat
MARC
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| 100 | 1 | |a Lasiecka, I. |q (Irena), |d 1948- | |
| 245 | 1 | 0 | |a Control theory for partial differential equations : |b continuous and approximation theories. |n 2, |p Abstract hyperbolic-like systems over a finite time horizon / |c Irena Lasiecka, Roberto Triggiani. |
| 246 | 3 | 0 | |a Abstract hyperbolic-like systems over a finite time horizon |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2000. | ||
| 300 | |a 1 online resource (xxi, pages 645-1067, [5] pages) : |b illustrations | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v v. 75 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a ""Cover""; ""Half Title""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""7 Some Auxiliary Results on Abstract Equations""; ""7.1 Mathematical Setting and Standing Assumptions""; ""7.2 Regularity of Land L * on [0, T]""; ""7.3 A Lifting Regularity Property When eAt Is a Group""; ""7.4 Extension of Regularity of Land L* on [0, â?ž] When eAt Is Uniformly Stable""; ""7.4.1 Direct Statement; Direct Proof""; ""7.4.2 Dual Statement; Dual Proof"" | |
| 505 | 8 | |a 7.5 Generation and Abstract Trace Regularity under Unbounded Perturbation7.6 Regularity of a Class of Abstract Damped Systems -- 7.6.1 Mathematical Setting and Assumptions -- 7.6.2 Main Regularity Results -- 7.6.3 Proof of Theorem 7.6.2.2: Dual Statement (7.6.2.6) -- 7.7 Illustrations of Theorem 7.6.2.2 to Boundary Damped Wave Equations -- 7.7.1 Wave Equation with Boundary Damping in the Neumann Be -- 7.7.2 Wave Equation with Boundary Damping in the Dirichlet BC -- Notes on Chapter 7 -- References and Bibliography | |
| 505 | 8 | |a ""8 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: The Case Where the Input â?? Solution Map Is Unbounded, but the Input â?? Observation Map Is Bounded""""8.1 Mathematical Setting and Formulation of the Problem""; ""8.2 Statement of Main Results""; ""8.2.1 The General Case: Theorem 8.2.1.1, Theorem 8.2.1.2, and Theorem 8.2.1.3""; ""8.2.2 The Regular Case: Theorem 8.2.2.1""; ""8.3 The General Case. A First Proof of Theorems 8.2.1.1 and 8.2.1.2 by a Variational Approach: From the Optimal Control Problem to the DRE and the IRE Theorem 8.2.1.3"" | |
| 505 | 8 | |a ""8.3.1 Explicit Representation Formulas for the Optimal Pair {uo, yo} under (h.1), (h.3)""""8.3.2 Estimates on uo ( • ,t; x) and Ryo ( . ,t; x). The Operator Î? ( . , . )""; ""8.3.3 Definition of P(t) and Preliminary Properties""; ""8.3.4 P(t) Solves the Differential Riccati Equation (8.2.1.32)""; ""8.3.5 Differential and Integral Riccati Equations""; ""8.3.6 The IRE without Passing through the DRE""; ""8.3.7 Uniqueness""; ""8.3.8 Proof of Theorem 8.2.1.3""; ""8.4 A Second Direct Proof of Theorem 8.2.1.2: From the Well-Posedness of the IRE to the Control Problem. Dynamic Programming"" | |
| 505 | 8 | |a 8.4.1 Existence and Uniqueness: Preliminaries8.4.2 Unique Local Solution to Eqn. (8.4.1.5)for Q(t, s) -- 8.4.3 Unique Local Solution to Eqn. (8.4.1. 7) for V(t). Global Solution P(t) under (h.1), (h.2) -- 8.4.4 Global A Priori Estimates for V and Q. Global Solution P(t) under (H. 1), (H.2), and (H.3) -- 8.4.5 Recovering the Optimal Control Problem under (H.I), (H.2), and (H.3) for (h.I) and (h.2)] -- 8.5 Proof of Theorem 8.2.2.1: The More Regular Case -- 8.5.1 A Preliminary Lemma -- 8.5.2 Completion of the Proof of Theorem 8.2.2.1 -- 8.5.3 An Auxiliary Lemma | |
| 650 | 0 | |a Differential equations, Partial. |0 http://id.loc.gov/authorities/subjects/sh85037912 | |
| 650 | 0 | |a Control theory. |0 http://id.loc.gov/authorities/subjects/sh85031658 | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 6 | |a Théorie de la commande. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
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| 650 | 7 | |a Differential equations, Partial |2 fast | |
| 650 | 7 | |a Hyperbolische Differentialgleichung |2 gnd |0 http://d-nb.info/gnd/4131213-2 | |
| 700 | 1 | |a Triggiani, R. |q (Roberto), |d 1942- | |
| 776 | 0 | 8 | |i Print version: |a Lasiecka, I. (Irena), 1948- |t Control theory for partial differential equations : 2, Abstract hyperbolic-like systems over a finite time horizon. |d Cambridge : Cambridge University Press, 2000 |z 0521584019 |w (DLC) 99011617 |w (OCoLC)316647885 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v v. 75. | |
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| author | Lasiecka, I. (Irena), 1948- |
| author2 | Triggiani, R. (Roberto), 1942- |
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| contents | ""Cover""; ""Half Title""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""7 Some Auxiliary Results on Abstract Equations""; ""7.1 Mathematical Setting and Standing Assumptions""; ""7.2 Regularity of Land L * on [0, T]""; ""7.3 A Lifting Regularity Property When eAt Is a Group""; ""7.4 Extension of Regularity of Land L* on [0, â?ž] When eAt Is Uniformly Stable""; ""7.4.1 Direct Statement; Direct Proof""; ""7.4.2 Dual Statement; Dual Proof"" 7.5 Generation and Abstract Trace Regularity under Unbounded Perturbation7.6 Regularity of a Class of Abstract Damped Systems -- 7.6.1 Mathematical Setting and Assumptions -- 7.6.2 Main Regularity Results -- 7.6.3 Proof of Theorem 7.6.2.2: Dual Statement (7.6.2.6) -- 7.7 Illustrations of Theorem 7.6.2.2 to Boundary Damped Wave Equations -- 7.7.1 Wave Equation with Boundary Damping in the Neumann Be -- 7.7.2 Wave Equation with Boundary Damping in the Dirichlet BC -- Notes on Chapter 7 -- References and Bibliography ""8 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: The Case Where the Input â?? Solution Map Is Unbounded, but the Input â?? Observation Map Is Bounded""""8.1 Mathematical Setting and Formulation of the Problem""; ""8.2 Statement of Main Results""; ""8.2.1 The General Case: Theorem 8.2.1.1, Theorem 8.2.1.2, and Theorem 8.2.1.3""; ""8.2.2 The Regular Case: Theorem 8.2.2.1""; ""8.3 The General Case. A First Proof of Theorems 8.2.1.1 and 8.2.1.2 by a Variational Approach: From the Optimal Control Problem to the DRE and the IRE Theorem 8.2.1.3"" ""8.3.1 Explicit Representation Formulas for the Optimal Pair {uo, yo} under (h.1), (h.3)""""8.3.2 Estimates on uo ( • ,t; x) and Ryo ( . ,t; x). The Operator Î? ( . , . )""; ""8.3.3 Definition of P(t) and Preliminary Properties""; ""8.3.4 P(t) Solves the Differential Riccati Equation (8.2.1.32)""; ""8.3.5 Differential and Integral Riccati Equations""; ""8.3.6 The IRE without Passing through the DRE""; ""8.3.7 Uniqueness""; ""8.3.8 Proof of Theorem 8.2.1.3""; ""8.4 A Second Direct Proof of Theorem 8.2.1.2: From the Well-Posedness of the IRE to the Control Problem. Dynamic Programming"" 8.4.1 Existence and Uniqueness: Preliminaries8.4.2 Unique Local Solution to Eqn. (8.4.1.5)for Q(t, s) -- 8.4.3 Unique Local Solution to Eqn. (8.4.1. 7) for V(t). Global Solution P(t) under (h.1), (h.2) -- 8.4.4 Global A Priori Estimates for V and Q. Global Solution P(t) under (H. 1), (H.2), and (H.3) -- 8.4.5 Recovering the Optimal Control Problem under (H.I), (H.2), and (H.3) for (h.I) and (h.2)] -- 8.5 Proof of Theorem 8.2.2.1: The More Regular Case -- 8.5.1 A Preliminary Lemma -- 8.5.2 Completion of the Proof of Theorem 8.2.2.1 -- 8.5.3 An Auxiliary Lemma |
| ctrlnum | (OCoLC)854919480 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn854919480 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:28Z |
| institution | BVB |
| isbn | 9781107089013 1107089018 |
| language | English |
| oclc_num | 854919480 |
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| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Lasiecka, I. (Irena), 1948- Control theory for partial differential equations : continuous and approximation theories. 2, Abstract hyperbolic-like systems over a finite time horizon / Irena Lasiecka, Roberto Triggiani. Abstract hyperbolic-like systems over a finite time horizon Cambridge : Cambridge University Press, 2000. 1 online resource (xxi, pages 645-1067, [5] pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 75 Includes bibliographical references and index. Print version record. ""Cover""; ""Half Title""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""7 Some Auxiliary Results on Abstract Equations""; ""7.1 Mathematical Setting and Standing Assumptions""; ""7.2 Regularity of Land L * on [0, T]""; ""7.3 A Lifting Regularity Property When eAt Is a Group""; ""7.4 Extension of Regularity of Land L* on [0, â?ž] When eAt Is Uniformly Stable""; ""7.4.1 Direct Statement; Direct Proof""; ""7.4.2 Dual Statement; Dual Proof"" 7.5 Generation and Abstract Trace Regularity under Unbounded Perturbation7.6 Regularity of a Class of Abstract Damped Systems -- 7.6.1 Mathematical Setting and Assumptions -- 7.6.2 Main Regularity Results -- 7.6.3 Proof of Theorem 7.6.2.2: Dual Statement (7.6.2.6) -- 7.7 Illustrations of Theorem 7.6.2.2 to Boundary Damped Wave Equations -- 7.7.1 Wave Equation with Boundary Damping in the Neumann Be -- 7.7.2 Wave Equation with Boundary Damping in the Dirichlet BC -- Notes on Chapter 7 -- References and Bibliography ""8 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: The Case Where the Input â?? Solution Map Is Unbounded, but the Input â?? Observation Map Is Bounded""""8.1 Mathematical Setting and Formulation of the Problem""; ""8.2 Statement of Main Results""; ""8.2.1 The General Case: Theorem 8.2.1.1, Theorem 8.2.1.2, and Theorem 8.2.1.3""; ""8.2.2 The Regular Case: Theorem 8.2.2.1""; ""8.3 The General Case. A First Proof of Theorems 8.2.1.1 and 8.2.1.2 by a Variational Approach: From the Optimal Control Problem to the DRE and the IRE Theorem 8.2.1.3"" ""8.3.1 Explicit Representation Formulas for the Optimal Pair {uo, yo} under (h.1), (h.3)""""8.3.2 Estimates on uo ( • ,t; x) and Ryo ( . ,t; x). The Operator Î? ( . , . )""; ""8.3.3 Definition of P(t) and Preliminary Properties""; ""8.3.4 P(t) Solves the Differential Riccati Equation (8.2.1.32)""; ""8.3.5 Differential and Integral Riccati Equations""; ""8.3.6 The IRE without Passing through the DRE""; ""8.3.7 Uniqueness""; ""8.3.8 Proof of Theorem 8.2.1.3""; ""8.4 A Second Direct Proof of Theorem 8.2.1.2: From the Well-Posedness of the IRE to the Control Problem. Dynamic Programming"" 8.4.1 Existence and Uniqueness: Preliminaries8.4.2 Unique Local Solution to Eqn. (8.4.1.5)for Q(t, s) -- 8.4.3 Unique Local Solution to Eqn. (8.4.1. 7) for V(t). Global Solution P(t) under (h.1), (h.2) -- 8.4.4 Global A Priori Estimates for V and Q. Global Solution P(t) under (H. 1), (H.2), and (H.3) -- 8.4.5 Recovering the Optimal Control Problem under (H.I), (H.2), and (H.3) for (h.I) and (h.2)] -- 8.5 Proof of Theorem 8.2.2.1: The More Regular Case -- 8.5.1 A Preliminary Lemma -- 8.5.2 Completion of the Proof of Theorem 8.2.2.1 -- 8.5.3 An Auxiliary Lemma 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 Hyperbolische Differentialgleichung gnd http://d-nb.info/gnd/4131213-2 Triggiani, R. (Roberto), 1942- Print version: Lasiecka, I. (Irena), 1948- Control theory for partial differential equations : 2, Abstract hyperbolic-like systems over a finite time horizon. Cambridge : Cambridge University Press, 2000 0521584019 (DLC) 99011617 (OCoLC)316647885 Encyclopedia of mathematics and its applications ; v. 75. FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569393 Volltext |
| spellingShingle | Lasiecka, I. (Irena), 1948- Control theory for partial differential equations : continuous and approximation theories. Encyclopedia of mathematics and its applications ; ""Cover""; ""Half Title""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""7 Some Auxiliary Results on Abstract Equations""; ""7.1 Mathematical Setting and Standing Assumptions""; ""7.2 Regularity of Land L * on [0, T]""; ""7.3 A Lifting Regularity Property When eAt Is a Group""; ""7.4 Extension of Regularity of Land L* on [0, â?ž] When eAt Is Uniformly Stable""; ""7.4.1 Direct Statement; Direct Proof""; ""7.4.2 Dual Statement; Dual Proof"" 7.5 Generation and Abstract Trace Regularity under Unbounded Perturbation7.6 Regularity of a Class of Abstract Damped Systems -- 7.6.1 Mathematical Setting and Assumptions -- 7.6.2 Main Regularity Results -- 7.6.3 Proof of Theorem 7.6.2.2: Dual Statement (7.6.2.6) -- 7.7 Illustrations of Theorem 7.6.2.2 to Boundary Damped Wave Equations -- 7.7.1 Wave Equation with Boundary Damping in the Neumann Be -- 7.7.2 Wave Equation with Boundary Damping in the Dirichlet BC -- Notes on Chapter 7 -- References and Bibliography ""8 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: The Case Where the Input â?? Solution Map Is Unbounded, but the Input â?? Observation Map Is Bounded""""8.1 Mathematical Setting and Formulation of the Problem""; ""8.2 Statement of Main Results""; ""8.2.1 The General Case: Theorem 8.2.1.1, Theorem 8.2.1.2, and Theorem 8.2.1.3""; ""8.2.2 The Regular Case: Theorem 8.2.2.1""; ""8.3 The General Case. A First Proof of Theorems 8.2.1.1 and 8.2.1.2 by a Variational Approach: From the Optimal Control Problem to the DRE and the IRE Theorem 8.2.1.3"" ""8.3.1 Explicit Representation Formulas for the Optimal Pair {uo, yo} under (h.1), (h.3)""""8.3.2 Estimates on uo ( • ,t; x) and Ryo ( . ,t; x). The Operator Î? ( . , . )""; ""8.3.3 Definition of P(t) and Preliminary Properties""; ""8.3.4 P(t) Solves the Differential Riccati Equation (8.2.1.32)""; ""8.3.5 Differential and Integral Riccati Equations""; ""8.3.6 The IRE without Passing through the DRE""; ""8.3.7 Uniqueness""; ""8.3.8 Proof of Theorem 8.2.1.3""; ""8.4 A Second Direct Proof of Theorem 8.2.1.2: From the Well-Posedness of the IRE to the Control Problem. Dynamic Programming"" 8.4.1 Existence and Uniqueness: Preliminaries8.4.2 Unique Local Solution to Eqn. (8.4.1.5)for Q(t, s) -- 8.4.3 Unique Local Solution to Eqn. (8.4.1. 7) for V(t). Global Solution P(t) under (h.1), (h.2) -- 8.4.4 Global A Priori Estimates for V and Q. Global Solution P(t) under (H. 1), (H.2), and (H.3) -- 8.4.5 Recovering the Optimal Control Problem under (H.I), (H.2), and (H.3) for (h.I) and (h.2)] -- 8.5 Proof of Theorem 8.2.2.1: The More Regular Case -- 8.5.1 A Preliminary Lemma -- 8.5.2 Completion of the Proof of Theorem 8.2.2.1 -- 8.5.3 An Auxiliary Lemma 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 Hyperbolische Differentialgleichung gnd http://d-nb.info/gnd/4131213-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037912 http://id.loc.gov/authorities/subjects/sh85031658 http://d-nb.info/gnd/4131213-2 |
| title | Control theory for partial differential equations : continuous and approximation theories. |
| title_alt | Abstract hyperbolic-like systems over a finite time horizon |
| 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. 2, Abstract hyperbolic-like systems over a finite time horizon / Irena Lasiecka, Roberto Triggiani. |
| title_fullStr | Control theory for partial differential equations : continuous and approximation theories. 2, Abstract hyperbolic-like systems over a finite time horizon / Irena Lasiecka, Roberto Triggiani. |
| title_full_unstemmed | Control theory for partial differential equations : continuous and approximation theories. 2, Abstract hyperbolic-like systems over a finite time horizon / 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 hyperbolic like systems over a finite time horizon |
| 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 Hyperbolische Differentialgleichung gnd http://d-nb.info/gnd/4131213-2 |
| topic_facet | Differential equations, Partial. Control theory. Équations aux dérivées partielles. Théorie de la commande. MATHEMATICS Differential Equations Partial. Control theory Differential equations, Partial Hyperbolische Differentialgleichung |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569393 |
| work_keys_str_mv | AT lasieckai controltheoryforpartialdifferentialequationscontinuousandapproximationtheories2 AT triggianir controltheoryforpartialdifferentialequationscontinuousandapproximationtheories2 AT lasieckai abstracthyperboliclikesystemsoverafinitetimehorizon AT triggianir abstracthyperboliclikesystemsoverafinitetimehorizon |