Optimality conditions for parabolic control problems and applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Leipzig
Teubner
1984
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Teubner-Texte zur Mathematik
62 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000243657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 164 S. graph. Darst. |
| ISSN: | 0138-502X |
Internformat
MARC
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| 100 | 1 | |a Tröltzsch, Fredi |d 1951- |e Verfasser |0 (DE-588)109612949 |4 aut | |
| 245 | 1 | 0 | |a Optimality conditions for parabolic control problems and applications |c Fredi Tröltzsch |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Leipzig |b Teubner |c 1984 | |
| 300 | |a 164 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 62 |x 0138-502X | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Differential equations, Parabolic | |
| 650 | 4 | |a Multipliers (Mathematical analysis) | |
| 650 | 0 | 7 | |a Nichtlineare parabolische Differentialgleichung |0 (DE-588)4455524-6 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1819301343361236992 |
|---|---|
| adam_text | CONTENTS
1. On necessary optimality conditions 7
1.1. Introduction 7
1.2. Regularity conditions and Lagrange multiplier rules . . 9
1.3. Application to non linear optimal control problems with
constraints on the control and the state 18
2. Optimal control of non linear Hammerstein integral equations
in Banach spaces 28
2.1. Spaces of abstract functions 28
2.2. Nemytski operators in Banach spaces 31
2.3. Linear Volterra integral equations in Banach spaces . . 32
2.4. The optimal control problem 38
2.5. Necessary optimality conditions 41
3. Evolution equations 50
3.1. Strongly continuous semigroups 50
3.2. Parabolic equations 54
3.3. Adjoint semigroup and adjoint evolution equation ... 56
3.4. Sobolev spaces Hm(£ ) and h£(£ ) 58
3.5. Operators generated by continuous bilinear forms ... 59
3.6. Second order elliptic differential operators and the
Dlrichlet problem 63
3.7. References 69
4. Optimal control of semilinear evolution equations 70
4.1. The optimal control problem 70
4.2. Necessary optimality conditions 73
4.3. Backward uniqueness property and backward uniqueness
property with respect to a convex cone for parabolic
equations 78
4.4. Bang bang principle and generalized bang bang principle 86
4.5. Linear time optimal control 94
4.6. Application 1 optimality conditions and generalized
bang bang principle for a linear distributed parabolic
control problem 100
4.7. Application 2 optimality conditions for a non linear
distributed parabolic control problem 104
4.8. More general boundary conditions 109
4.9. References 110
5
5. Optimal boundary control of parabolic equations 112
5.1. The optimal control problem 112
5.2. Necessary optimality conditions 116
5.3. Unique continuation for parabolic equations and rela¬
ted problems 120
5.4. Bang bang principle and generalized bang bang principle 124
5.5. Linear time optimal boundary control problems .... 131
5.6. Integral operators generated by Green s functions . . 134
5.7. Miscellaneous problems 138
5.7.1. Control depending only on the time 138
5.7.2. Final approximation by the maximum norm .... 140
5.7.3. Domain £2 of dimension one 141
5.8. References 152
Notations . 154
Bibliography 156
6
|
| any_adam_object | 1 |
| author | Tröltzsch, Fredi 1951- |
| author_GND | (DE-588)109612949 |
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| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8/312 |
| dewey-search | 629.8/312 |
| dewey-sort | 3629.8 3312 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| edition | 1. Aufl. |
| format | Book |
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| id | DE-604.BV000392405 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:20:16Z |
| institution | BVB |
| issn | 0138-502X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000243657 |
| oclc_num | 11665661 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-739 DE-29T DE-634 DE-11 DE-188 DE-706 |
| owner_facet | DE-12 DE-384 DE-703 DE-739 DE-29T DE-634 DE-11 DE-188 DE-706 |
| physical | 164 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spellingShingle | Tröltzsch, Fredi 1951- Optimality conditions for parabolic control problems and applications Teubner-Texte zur Mathematik Control theory Differential equations, Parabolic Multipliers (Mathematical analysis) Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4455524-6 (DE-588)4032317-1 (DE-588)4173245-5 (DE-588)4121428-6 |
| title | Optimality conditions for parabolic control problems and applications |
| title_auth | Optimality conditions for parabolic control problems and applications |
| title_exact_search | Optimality conditions for parabolic control problems and applications |
| title_full | Optimality conditions for parabolic control problems and applications Fredi Tröltzsch |
| title_fullStr | Optimality conditions for parabolic control problems and applications Fredi Tröltzsch |
| title_full_unstemmed | Optimality conditions for parabolic control problems and applications Fredi Tröltzsch |
| title_short | Optimality conditions for parabolic control problems and applications |
| title_sort | optimality conditions for parabolic control problems and applications |
| topic | Control theory Differential equations, Parabolic Multipliers (Mathematical analysis) Nichtlineare parabolische Differentialgleichung (DE-588)4455524-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Control theory Differential equations, Parabolic Multipliers (Mathematical analysis) Nichtlineare parabolische Differentialgleichung Kontrolltheorie Parabolische Differentialgleichung Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000243657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT troltzschfredi optimalityconditionsforparaboliccontrolproblemsandapplications |