Exact controllability and stabilization: the multiplier method
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley [u.a.]
1994
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| Series: | Research in applied mathematics
36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 156 S. |
| ISBN: | 222584612X 0471953679 |
Staff View
MARC
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| 100 | 1 | |a Komornik, Vilmos |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Exact controllability and stabilization |b the multiplier method |c V. Komornik |
| 264 | 1 | |a Chichester [u.a.] |b Wiley [u.a.] |c 1994 | |
| 300 | |a VIII, 156 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Multipliers (Mathematical analysis) | |
| 650 | 4 | |a Wave equation |x Numerical solutions | |
| 650 | 0 | 7 | |a Kontrolltheorie |0 (DE-588)4032317-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804124277268545536 |
|---|---|
| adam_text | vii
TABLE OF CONTENTS
Preface v
0. Introduction. Vibrating strings 1
1. Linear evolutionary problems 7
1.1. The diagram VcH = H CV 7
1.2. The equation u + Au = 0 10
1.3. The wave equation 11
1.4. A Petrovsky system 13
1.5. Another Petrovsky system 15
2. Hidden regularity. Weak solutions 18
2.1. A special vector field 18
2.2. The wave equation. The multiplier method 19
2.3. The first Petrovsky system 24
2.4. The second Petrovsky system 29
3. Uniqueness theorems 35
3.1. The wave equation. Dirichlet condition 35
3.2. The first Petrovsky system 40
3.3. The second Petrovsky system 44
3.4. The wave equation. Mixed boundary conditions 47
4. Exact controllability. Hilbert uniqueness method .... 53
4.1. The wave equation. Dirichlet control 53
4.2. The first Petrovsky system 57
4.3. The wave equation. Neumann or Robin control 59
5. Norm inequalities 63
5.1. Riesz sequences 63
5.2. Formulation of the results 65
5.3. Proof of theorem 5.3 69
5.4. Proof of theorem 5.5 73
6. New uniqueness and exact controllability results .... 75
6.1. A unique continuation theorem 75
6.2. The wave equation. Dirichlet condition 77
6.3. The first Petrovsky system 79
viii
6.4. The second Petrovsky system. Uniqueness theorems 81
6.5. The second Petrovsky system. Exact controllability 83
6.6. The wave equation. Neumann or Robin condition 85
7. Dissipative evolutionary systems 00
7.1. Maximal monotone operators 90
7.2. The wave equation 91
7.3. Kirchhoff plates 97
8. Linear stabilization 103
8.1. An integral inequality 103
8.2. Uniform stabilization of the wave equation I 104
8.3. Links with the exact controllability. Russell s principle 108
8.4. Uniform stabilization of the wave equation II Ill
8.5. Strong stabilization. LaSalle s principle 114
8.6. Uniform stabilization of the wave equation III 116
8.7. Uniform stabilization of Maxwell s equations 118
9. Nonlinear stabilization 124
9.1. A nonlinear integral inequality 124
9.2. Uniform stabilization of the wave equation I 126
9.3. Uniform stabilization of the wave equation II 134
9.4. Uniform stabilization of Kirchhoff plates 135
10. Internal stabilization of the Korteweg—de Vries equation 144
10.1. Well posedness and conservation laws 144
10.2. Uniform stabilization by linear feedbacks 146
References 152
|
| any_adam_object | 1 |
| author | Komornik, Vilmos |
| author_facet | Komornik, Vilmos |
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| author_sort | Komornik, Vilmos |
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| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV009912790 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:06Z |
| institution | BVB |
| isbn | 222584612X 0471953679 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006566698 |
| oclc_num | 31649985 |
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| owner | DE-703 DE-12 DE-706 DE-634 DE-83 |
| owner_facet | DE-703 DE-12 DE-706 DE-634 DE-83 |
| physical | VIII, 156 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Wiley [u.a.] |
| record_format | marc |
| series | Research in applied mathematics |
| series2 | Research in applied mathematics |
| spelling | Komornik, Vilmos Verfasser aut Exact controllability and stabilization the multiplier method V. Komornik Chichester [u.a.] Wiley [u.a.] 1994 VIII, 156 S. txt rdacontent n rdamedia nc rdacarrier Research in applied mathematics 36 Equation d'onde - Solutions numériques ram Multiplicateurs (Analyse mathématique) ram Problèmes aux limites ram Boundary value problems Numerical solutions Multipliers (Mathematical analysis) Wave equation Numerical solutions Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Verteiltes System (DE-588)4238872-7 gnd rswk-swf Verteiltes System (DE-588)4238872-7 s Stabilität (DE-588)4056693-6 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Research in applied mathematics 36 (DE-604)BV002654185 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006566698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Komornik, Vilmos Exact controllability and stabilization the multiplier method Research in applied mathematics Equation d'onde - Solutions numériques ram Multiplicateurs (Analyse mathématique) ram Problèmes aux limites ram Boundary value problems Numerical solutions Multipliers (Mathematical analysis) Wave equation Numerical solutions Kontrolltheorie (DE-588)4032317-1 gnd Stabilität (DE-588)4056693-6 gnd Verteiltes System (DE-588)4238872-7 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4056693-6 (DE-588)4238872-7 |
| title | Exact controllability and stabilization the multiplier method |
| title_auth | Exact controllability and stabilization the multiplier method |
| title_exact_search | Exact controllability and stabilization the multiplier method |
| title_full | Exact controllability and stabilization the multiplier method V. Komornik |
| title_fullStr | Exact controllability and stabilization the multiplier method V. Komornik |
| title_full_unstemmed | Exact controllability and stabilization the multiplier method V. Komornik |
| title_short | Exact controllability and stabilization |
| title_sort | exact controllability and stabilization the multiplier method |
| title_sub | the multiplier method |
| topic | Equation d'onde - Solutions numériques ram Multiplicateurs (Analyse mathématique) ram Problèmes aux limites ram Boundary value problems Numerical solutions Multipliers (Mathematical analysis) Wave equation Numerical solutions Kontrolltheorie (DE-588)4032317-1 gnd Stabilität (DE-588)4056693-6 gnd Verteiltes System (DE-588)4238872-7 gnd |
| topic_facet | Equation d'onde - Solutions numériques Multiplicateurs (Analyse mathématique) Problèmes aux limites Boundary value problems Numerical solutions Multipliers (Mathematical analysis) Wave equation Numerical solutions Kontrolltheorie Stabilität Verteiltes System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006566698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002654185 |
| work_keys_str_mv | AT komornikvilmos exactcontrollabilityandstabilizationthemultipliermethod |