Control theory for partial differential equations: continuous and approximation theories 1 Abstract parabolic systems
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
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Cambridge
Cambridge Univ. Press
2000
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| Ausgabe: | 1. published |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
74 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxi, 644 Seiten |
| ISBN: | 0521434084 9780521434089 9780521155670 |
Internformat
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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 |
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| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2000 | |
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| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 74 | |
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Datensatz im Suchindex
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| adam_text | IMAGE 1
E N C Y C L O P E D IA OF M A T H E M A T I CS AND ITS A P P L I C A T I
O NS
CONTROL THEORYFOR PARTIAL DIFFERENTIAL
EQUATIONS: CONTINUOUS AND APPROXIMATION THEORIES I: ABSTRACT PARABOLIC
SYSTEMS
IRENA LASIECKA ROBERTO TRIGGIANI
H CAMBRIDGE
UNIVERSITY PRESS
IMAGE 2
CONTENTS
PREFACE PAGE XV
0 BACKGROUND 1
0. 1 SOME FUNCTION SPACES USED IN CHAPTER 1 3
0.2 REGULARITY OF THE VARIATION OF PARAMETER FORMULA WHEN E AT IS A S.C.
ANALYTIC SEMIGROUP 3
0.3 THE EXTRAPOLATION SPACE [V(A*)] 6
0.4 ABSTRACT SETTING FOR VOLUME I. THE OPERATOR L T IN (1.1.9), OR L ST
IN (1.4.1.6), OF CHAPTER 1 7
REFERENCES AND BIBLIOGRAPHY 9
1 OPTIMAL QUADRATIC COST PROBLEM OVER A PREASSIGNED FINITE TIME
INTERVAL: DIFFERENTIAL RICCATI EQUATION 11
1.1 MATHEMATICAL SETTING AND FORMULATION OF THE PROBLEM 12
1.2 STATEMENT OF MAIN RESULTS 14
1.3 ORIENTATION 21
1.4 PROOF OF THEOREM 1.2.1.1 WITH GL T CLOSED 23
1.5 FIRSTSMOOTHINGCASEOFTHEOPERATORG: THECASE (-A*) SS G*G E C(Y), SS 2Y
- 1. PROOF OF THEOREM 1.2.2.1 75
1.6 A SECOND SMOOTHING CASE OF THE OPERATOR G: THE CASE {-A*Y G*G E
C(Y). PROOF OF THEOREM 1.2.2.2 97
1.7 THE THEORY OF THEOREM 1.2.1.1 IS SHARP. COUNTEREXAMPLES WHEN GL T IS
NOT CLOSABLE 99
1.8 EXTENSION TO UNBOUNDED OPERATORS R AND G 103
1A PROOF OF LEMMA 1.5.L.L(III) 112
NOTES ON CHAPTER 1 113
GLOSSARY OF SYMBOLS FOR CHAPTER 1 118
REFERENCES AND BIBLIOGRAPHY 119
2 OPTIMAL QUADRATIC COST PROBLEM OVER AN INFINITE TIME INTERVAL:
ALGEBRAIC RICCATI EQUATION 121
2.1 MATHEMATICAL SETTING AND FORMULATION OF THE PROBLEM 122
IMAGE 3
VM
CONTENTS
2.2 STATEMENT OF MAIN RESULTS 125
2.3 PROOFOF THEOREM 2.2.1 129
2.4 PROOF OF THEOREM 2.2.2: EXPONENTIAL STABILITY OF $ (?) AND
UNIQUENESS OF THE SOLUTION OF THE ALGEBRAIC RICCATI EQUATION UNDER THE
DETECTABILITY CONDITION (2.1.13) 155
2.5 EXTENSIONS TO UNBOUNDED R : R E (D(AE S ); Z), 8 MIN{L-Y,} 160
2A BOUNDED INVERSION OF [/ + SV], S, V 0 167
2B THE CASE 0 = 1 IN (2.3.7.4) WHEN A IS SELF-ADJOINT AND R = I 168
NOTES ON CHAPTER 2 170
GLOSSARY OF SYMBOLS FOR CHAPTER 2 175
REFERENCES AND BIBLIOGRAPHY 176
ILLUSTRATIONS OF THE ABSTRACT THEORY OF CHAPTERS 1 AND 2 TO PARTIAL
DIFFERENTIAL EQUATIONS WITH BOUNDARY/POINT CONTROLS 178
3.0 EXAMPLES OF PARTIAL DIFFERENTIAL EQUATION PROBLEMS SATISFYING
CHAPTERS 1 AND 2 179
3.1 HEAT EQUATION WITH DIRICHLET BOUNDARY CONTROL: RICCATI THEORY 180
3.2 HEAT EQUATION WITH DIRICHLET BOUNDARY CONTROL: REGULARITY THEORY OF
THE OPTIMAL PAIR 187
3.3 HEAT EQUATION WITH NEUMANN BOUNDARY CONTROL 194
3.4 A STRUCTURALLY DAMPED PLATELIKE EQUATION WITH POINT CONTROL AND
SIMPLIFIED HINGED BC 204
3.5 KELVIN-VOIGHT PLATELIKE EQUATION WITH POINT CONTROL WITH FREE BC 208
3.6 A STRUCTURALLY DAMPED PLATELIKE EQUATION WITH BOUNDARY CONTROL IN
THE SIMPLIFIED MOMENT BC 211
3.7 ANOTHER PLATELIKE EQUATION WITH POINT CONTROL AND CLAMPED BC 214 3.8
THE STRONGLY DAMPED WAVE EQUATION WITH POINT CONTROL AND DIRICHLET BC
216
3.9 A STRUCTURALLY DAMPED KIRCHHOFF EQUATION WITH POINT CONTROL ACTING
THROUGH $(* -X) AND SIMPLIFIED HINGED BC 218
3.10 A STRUCTURALLY DAMPED KIRCHHOFF EQUATION (REVISITED) WITH POINT
CONTROL ACTING THROUGH $ (* -X) AND SIMPLIFIED HINGED BC 221 3.11
THERMO-ELASTIC PLATES WITH THERMAL CONTROL AND HOMOGENEOUS CLAMPED
MECHANICAL BC 224
3.12 THERMO-ELASTIC PLATES WITH MECHANICAL CONTROL IN THE BENDING MOMENT
(HINGED BC) AND HOMOGENEOUS NEUMANN THERMAL BC 237 3.13 THERMO-ELASTIC
PLATES WITH MECHANICAL CONTROL AS A SHEAR FORCE (FREE BC) 248
3.14 STRUCTURALLY DAMPED EULER-BERNOULLI EQUATIONS WITH DAMPED FREE BC
AND POINT CONTROL OR BOUNDARY CONTROL 261
IMAGE 4
CONTENTS
IX
3.15 A LINEARIZED MODEL OF WELL/RESERVOIR COUPLING FOR A
MONOPHASIC FLOW WITH BOUNDARY CONTROL 269
3.16 ADDITIONAL ILLUSTRATIONS WITH CONTROL OPERATOR B AND OBSERVATION
OPERATOR R BOTH GENUINELY UNBOUNDED 278
3A INTERPOLATION (INTERMEDIATE) SOBOLEV SPACES AND THEIR IDENTIFICATION
WITH DOMAINS OF FRACTIONAL POWERS OF ELLIPTIC OPERATORS 282
3B DAMPED ELASTIC OPERATORS 285
3C BOUNDARY OPERATORS FOR BENDING MOMENTS AND SHEAR FORCES ON
TWO-DIMENSIONAL DOMAINS 296
3D CO-SEMIGROUP/ANALYTIC SEMIGROUP GENERATION WHEN A = AM, A POSITIVE
SELF-ADJOINT, M MATRIX. APPLICATIONS TO THERMO-ELASTIC EQUATIONS WITH
HINGED MECHANICAL BC AND DIRICHLET THERMAL BC 311
3E ANALYTICITY OF THE S.C. SEMIGROUPS ARISING FROM ABSTRACT
THERMO-ELASTIC EQUATIONS. FIRST PROOF 324
3F ANALYTICITY OF THE S.C. SEMIGROUP ARISING FROM ABSTRACT
THERMO-ELASTIC EQUATIONS. SECOND PROOF 346
3G ANALYTICITY OF THE S.C. SEMIGROUP ARISING FROM ABSTRACT
THERMO-ELASTIC EQUATIONS. THIRD PROOF 363
3H ANALYTICITY OF THE S.C. SEMIGROUP ARISING FROM PROBLEM (3.12.1)
(HINGED MECHANICAL BC/NEUMANN (ROBIN) THERMAL BC) 370
31 ANALYTICITY OF THE S.C. SEMIGROUP ARISING FROM PROBLEM (3.13.1) OF
SECTION 13 (FREE MECHANICAL BC/NEUMANN (ROBIN) THERMAL BC) 382 3J
UNIFORM EXPONENTIAL ENERGY DECAY OF THERMO-ELASTIC EQUATIONS WITH, OR
WITHOUT, ROTATIONAL TERM. ENERGY METHODS 402
NOTES ON CHAPTER 3 413
REFERENCES AND BIBLIOGRAPHY 425
NUMERICAL APPROXIMATIONS OF ALGEBRAIC RICCATI EQUATIONS 431
4.1 INTRODUCTION: CONTINUOUS AND DISCRETE OPTIMAL CONTROL PROBLEMS 431
4.2 BACKGROUND MATERIAL 444
4.3 CONVERGENCE PROPERTIES OF THE OPERATORS L H AND L* H ; L H AND L* H
446
4.4 PERTURBATION RESULTS 451
4.5 UNIFORM CONVERGENCE P H U H -* P AND B* H P H Y H - B*P 471
4.6 OPTIMAL RATES OF CONVERGENCE 484
4A A SHARP RESULT ON THE EXPONENTIAL OPERATOR-NORM DECAY OF A FAMILY OF
STRONGLY CONTINUOUS SEMIGROUPS 488
4B FINITE ELEMENT APPROXIMATIONS OF DYNAMIC COMPENSATORS OF LUENBERGER S
TYPE FOR PARTIALLY OBSERVED ANALYTIC SYSTEMS WITH FULLY UNBOUNDED
CONTROL AND OBSERVATION OPERATORS 495
NOTES ON CHAPTER 4 504
GLOSSARY OF SYMBOLS FOR CHAPTER 4 509
REFERENCES AND BIBLIOGRAPHY 509
IMAGE 5
X
CONTENTS
ILLUSTRATIONS OF THE NUMERICAL THEORY OF CHAPTER 4 TO PARABOLIC-LIKE
BOUNDARY/POINT CONTROL PDE PROBLEMS 511
5.1 INTRODUCTORY APPROXIMATION RESULTS 511
5.2 HEAT EQUATION WITH DIRICHLET BOUNDARY CONTROL 521
5.3 HEAT EQUATION WITH NEUMANN BOUNDARY CONTROL. OPTIMAL RATES OF
CONVERGENCE WITH R 1 AND GALERKIN APPROXIMATION 531
5.4 A STRUCTURALLY DAMPED PLATELIKE EQUATION WITH INTERIOR POINT CONTROL
WITH R 3 537
5.5 KELVIN-VOIGHT PLATELIKE EQUATION WITH INTERIOR POINT CONTROL WITH R
3 544
5.6 A STRUCTURALLY DAMPED PLATELIKE EQUATION WITH BOUNDARY CONTROL WITH
R 3 549
NOTES ON CHAPTER 5 554
GLOSSARY OF SYMBOLS FOR CHAPTER 5, SECTION 5.1 554
REFERENCES AND BIBLIOGRAPHY 554
MIN-MAX GAME THEORY OVER AN INFINITE TIME INTERVAL AND ALGEBRAIC RICCATI
EQUATIONS 556
PART I: GENERAL CASE 557
6.1 MATHEMATICAL SETTING; FORMULATION OF THE MIN-MAX GAME PROBLEM;
STATEMENT OF MAIN RESULTS 557
6.2 MINIMIZATION OF J WT J OVER U E L 2 (0, T; U) FOR W FIXED 562
6.3 MINIMIZATION OF J W 00 OVER U E L 2 (0, OO; U) FOR W FIXED: THE
LIMIT PROCESS AS T F OO 570
6.4 COLLECTION OF EXPLICIT FORMULAE FOR P WT00 , R WT0O , AND Y^ J0O IN
STABLEFORM 581
6.5 EXPLICIT EXPRESSION FOR THE OPTIMAL COST J^^IYO = 0) AS A QUADRATIC
TERM 583
6.6 DEFINITION OF THE CRITICAL VALUE Y C . COERCIVITY OF E Y FOR Y Y C
585
6.7 MAXIMIZATION OF J I00 OVER W DIRECTLY ON [0, OO] FOR Y Y C .
CHARACTERIZATION OF OPTIMAL QUANTITIES 586
6.8 EXPLICIT EXPRESSION OF W*(- ; YO) IN TERMS OF THE DATA VIA E~ X FOR
Y Y C 589
6.9 SMOOTHING PROPERTIES OF THE OPERATORS L, L*, W, W*: THE OPTIMAL U*,
Y*, W* ARE CONTINUOUS IN TIME 589
6.10 A TRANSITION PROPERTY FOR W* FOR Y Y C 593
6.11 A TRANSITION PROPERTY FOR R* FOR Y Y C 595
6.12 THE SEMIGROUP PROPERTY FOR Y* AND A TRANSITION PROPERTY FOR P* FOR
Y Y C 596
6.13 DEFINITION OF P AND ITS PROPERTIES 598
6.14 THE FEEDBACK GENERATOR A F AND ITS PRELIMINARY PROPERTIES FOR Y Y
C 600
IMAGE 6
CONTENTS
XI
6.15 THE OPERATOR P IS A SOLUTION OF THE ALGEBRAIC RICCATI EQUATION,
ARE K FOR Y YC 603
6.16 THE SEMIGROUP GENERATED BY (A - BB*P) IS UNIFORMLY STABLE 604 6.17
THE CASE 0 Y Y C : SUP J T00 (YO) = +OO 606
6.18 PROOFOF THEOREM 6.1.3.2 607
PART II: THE CASE WHERE E AT IS STABLE 608
6.19 MOTIVATION, STATEMENT OF MAIN RESULTS 608
6.20 MINIMIZATION OF J OVER U FOR W FIXED 612
6.21 MAXIMIZATION OF J(YO) OVER W: EXISTENCE OF A UNIQUE OPTIMAL W* 616
6.22 EXPLICIT EXPRESSIONS OF [U*, Y*, W*} AND P FOR Y Y C IN TERMS
OFTHE DATA VIA - 618
6.23 SMOOTHING PROPERTIES OFTHE OPERATORS L, L*, W, W*: THE OPTIMAL
U*,Y*, W* ARE CONTINUOUS IN TIME 620
6.24 A TRANSITION PROPERTY FOR W* FOR Y Y C 622
6.25 THE SEMIGROUP PROPERTY FOR Y* FOR Y Y C AND ITS STABILITY 626
6.26 THE RICCATI OPERATOR, P, FOR Y Y C 627
6A OPTIMAL CONTROL PROBLEM WITH NONDEFINITE QUADRATIC COST. THE STABLE,
ANALYTIC CASE. A BRIEF SKETCH 630
NOTES ON CHAPTER 6 639
REFERENCES AND BIBLIOGRAPHY 642
CONTENTS OF VOLUME II
SOME AUXILIARY RESULTS ON ABSTRACT EQUATIONS 645
7.1 MATHEMATICAL SETTING AND STANDING ASSUMPTIONS 645
7.2 REGULARITY OF L AND L* ON [0, T] 648
7.3 A LIFTING REGULARITY PROPERTY WHEN E AT IS A GROUP 651
7.4 EXTENSION OF REGULARITY OF L AND L* ON [0, OO] WHEN E AT IS
UNIFORMLY STABLE 653
7.5 GENERATION AND ABSTRACT TRACE REGULARITY UNDER UNBOUNDED
PERTURBATION 660
7.6 REGULARITY OF A CLASS OF ABSTRACT DAMPED SYSTEMS 663
7.7 ILLUSTRATIONS OF THEOREM 7.6.2.2 TO BOUNDARY DAMPED WAVE EQUATIONS
667
NOTES ON CHAPTER 7 671
REFERENCES AND BIBLIOGRAPHY 671
OPTIMAL QUADRATIC COST PROBLEM OVER A PREASSIGNED FINITE TIME INTERVAL:
THE CASE WHERE THE INPUT - * SOLUTION MAP IS UNBOUNDED, BUT THE INPUT
-** OBSERVATION MAP IS BOUNDED 673
8.1 MATHEMATICAL SETTING AND FORMULATION OF THE PROBLEM 675
8.2 STATEMENT OF MAIN RESULTS 679
IMAGE 7
XLL
CONTENTS
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 8.2.1.3 687
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 714
8.5 PROOF OF THEOREM 8.2.2.1: THE MORE REGULAER CASE 733
8.6 APPLICATION OF THEOREMS 8.2.1.1, 8.2.1.2, AND 8.2.2.1: NEUMANN
BOUNDARY CONTROL AND DIRICHLET BOUNDARY OBSERVATION FOR SECOND-ORDER
HYPERBOLIC EQUATIONS 736
8.7 A ONE-DIMENSIONAL HYPERBOLIC EQUATION WITH DIRICHLET CONTROL (B
UNBOUNDED) AND POINT OBSERVATION (R UNBOUNDED) THAT SATISFIES (H.L) AND
(H.3) BUT NOT (H.2), (H.L), (H.2), AND (H.3). YET, THE DRE IS TRIVIALLY
SATISFIED AS A LINEAR EQUATION 745
8A INTERIOR AND BOUNDARY REGULARITY OF MIXED PROBLEMS FOR SECOND-ORDER
HYPERBOLIC EQUATIONS WITH NEUMANN-TYPE BC 755 NOTES ON CHAPTER 8 761
REFERENCES AND BIBLIOGRAPHY 763
OPTIMAL QUADRATIC COST PROBLEM OVER A PREASSIGNED FINITE TIME INTERVAL:
THE CASE WHERE THE INPUT -** SOLUTION MAP IS BOUNDED. DIFFERENTIAL AND
INTEGRAL RICCATI EQUATIONS 765
9.1 MATHEMATICAL SETTING AND FORMULATION OF THE PROBLEM 765
9.2 STATEMENT OF MAIN RESULT: THEOREMS 9.2.1, 9.2.2, AND 9.2.3 772
9.3 PROOFS OF THEOREM 9.2.1 AND THEOREM 9.2.2 (BY THE VARIATIONAL
APPROACH AND BY THE DIRECT APPROACH). PROOF OF THEOREM 9.2.3 776 9.4
ISOMORPHISM OF P(T), 0 T T, AND EXACT CONTROUABILITY OF [A*, R*} ON
[0, T - T] WHEN G = 0 815
9.5 NONSMOOTHING OBSERVATION R: LIMIT SOLUTION OF THE DIFFERENTIAL
RICCATI EQUATION UNDER THE SOLE ASSUMPTION (A.L) WHEN G = 0 819
9.6 DUAL DIFFERENTIAL AND INTERGRAL RICCATI EQUATIONS WHEN A IS A GROUP
GENERATOR UNDER (A.L) AND R E C(Y; Z) AND G = 0. (BOUNDED CONTROL
OPERATOR, UNBOUNDED OBSERVATION) 825
9.7 OPTIMAL CONTROL PROBLEM WITH BOUNDED CONTROL OPERATOR AND UNBOUNDED
OBSERVATION OPERATOR 839
9.8 APPLICATION TO HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH POINT
CONTROL. REGULARITY THEORY 842
9.9 PROOF OF REGULARITY RESULTS NEEDED IN SECTION 9.8 861
9.10 A COUPLED SYSTEM OF A WAVE AND A KIRCHHOFF EQUATION WITH POINT
CONTROL, ARISING IN NOISE REDUCTION. REGULARITY THEORY 884
IMAGE 8
CONTENTS
XM
9.11 A COUPLED SYSTEM OF A WAVE AND A STRUCTURALLY DAMPED
EULER-BERNOULLI EQUATION WITH POINT CONTROL, ARISING IN NOISE REDUCTION.
REGULARITY THEORY 901
9A PROOF OF (9.9.1.16) IN LEMMA 9.9.1.1 908
9B PROOF OF (9.9.3.14) IN LEMMA 9.9.3.1 910
NOTES ON CHAPTER 9 913
REFERENCES AND BIBLIOGRAPHY 916
DIFFERENTIAL RICCATI EQUATIONS UNDER SLIGHTLY SMOOTHING OBSERVATION
OPERATOR. APPLICATIONS TO HYPERBOLIC AND PETROWSKI-TYPE PDES. REGULARITY
THEORY 919
10.1 MATHEMATICAL SETTING AND PROBLEM STATEMENT 920
10.2 STATEMENT OF THE MAIN RESULTS 926
10.3 PROOF OF THEOREMS 10.2.1 AND 10.2.2 928
10.4 PROOF OF THEOREM 10.2.3 936
10.5 APPLICATION: SECOND-ORDER HYPERBOLIC EQUATIONS WITH DIRICHLET
BOUNDARY CONTROL. REGULARITY THEORY 942
10.6 APPLICATION: NONSYMMETRIC, NONDISSIPATIVE FIRST-ORDER HYPERBOLIC
SYSTEMS WITH BOUNDARY CONTROL. REGULARITY THEORY 972 10.7 APPLICATION:
KIRCHOFF EQUATION WITH ONE BOUNDARY CONTROL. REGULARITY THEORY 989
10.8 APPLICATION: EULER-BERNOULLI EQUATION WITH ONE BOUNDARY CONTROL.
REGULARITY THEORY 1019
10.9 APPLICATION: SCHROEDINGER EQUATIONS WITH DIRICHLET BOUNDARY CONTROL.
REGULARITY THEORY 1042
NOTES ON CHAPTER 10 1059
GLOSSARY OF SELECTED SYMBOLS FOR CHAPTER 10 1065
REFERENCES AND BIBLIOGRAPHY 1065
|
| any_adam_object | 1 |
| author | Lasiecka, Irena 1948- Triggiani, Roberto 1942- |
| author_GND | (DE-588)111374383 (DE-588)112914292 |
| author_facet | Lasiecka, Irena 1948- Triggiani, Roberto 1942- |
| author_role | aut aut |
| author_sort | Lasiecka, Irena 1948- |
| author_variant | i l il r t rt |
| building | Verbundindex |
| bvnumber | BV013028412 |
| classification_rvk | SK 560 |
| classification_tum | MAT 356f |
| ctrlnum | (OCoLC)440588413 (DE-599)BVBBV013028412 |
| discipline | Mathematik |
| edition | 1. published |
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| id | DE-604.BV013028412 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:37:54Z |
| institution | BVB |
| isbn | 0521434084 9780521434089 9780521155670 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008875747 |
| oclc_num | 440588413 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-703 DE-384 DE-91G DE-BY-TUM DE-634 DE-11 DE-188 DE-83 |
| physical | xxi, 644 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Lasiecka, Irena 1948- Verfasser (DE-588)111374383 aut Control theory for partial differential equations continuous and approximation theories 1 Abstract parabolic systems Irena Lasiecka ; Roberto Triggiani 1. published Cambridge Cambridge Univ. Press 2000 xxi, 644 Seiten txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 74 Encyclopedia of mathematics and its applications ... Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 s DE-604 Triggiani, Roberto 1942- Verfasser (DE-588)112914292 aut (DE-604)BV013028395 1 Encyclopedia of mathematics and its applications 74 (DE-604)BV000903719 74 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008875747&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lasiecka, Irena 1948- Triggiani, Roberto 1942- Control theory for partial differential equations continuous and approximation theories Encyclopedia of mathematics and its applications Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4173245-5 |
| title | Control theory for partial differential equations continuous and approximation theories |
| 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 | Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008875747&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013028395 (DE-604)BV000903719 |
| work_keys_str_mv | AT lasieckairena controltheoryforpartialdifferentialequationscontinuousandapproximationtheories1 AT triggianiroberto controltheoryforpartialdifferentialequationscontinuousandapproximationtheories1 |