Controllability and observability for quasilinear hyperbolic systems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Springfield, MO
American Institute of Mathematical Sciences
2010
|
| Schriftenreihe: | AIMS on applied mathematics
3 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020319317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 222 S. Ill., graph. Darst. |
| ISBN: | 9787040241631 7040241633 |
Internformat
MARC
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| 100 | 1 | |a Li, Daqian |d 1937- |e Verfasser |0 (DE-588)124460550 |4 aut | |
| 245 | 1 | 0 | |a Controllability and observability for quasilinear hyperbolic systems |c Tatsien Li |
| 264 | 1 | |a Springfield, MO |b American Institute of Mathematical Sciences |c 2010 | |
| 300 | |a X, 222 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a AIMS on applied mathematics |v 3 | |
| 650 | 0 | 7 | |a Quasilineare hyperbolische Differentialgleichung |0 (DE-588)4651046-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Steuerbarkeit |0 (DE-588)4134713-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quasilineare hyperbolische Differentialgleichung |0 (DE-588)4651046-1 |D s |
| 689 | 0 | 1 | |a Steuerbarkeit |0 (DE-588)4134713-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a AIMS on applied mathematics |v 3 |w (DE-604)BV023094684 |9 3 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020319317 | |
Datensatz im Suchindex
| _version_ | 1819257296206692352 |
|---|---|
| adam_text | Contents
1
Introduction
............................................... 1
1.1
Exact Controllability
..................................... 1
1.2
Exact
Observability
...................................... 8
1.3
Duality Between Controllability and Observability
......... 12
1.4
Exact Boundary Controllability and Exact Boundary
Observability for 1-D
Quasilinear
Wave Equations
........... 13
1.5
Exact Boundary Controllability and Exact Boundary
Observability of Unsteady Flows in a Tree-Like Network of
Open Canals
............................................ 14
1.6
Nonautonomous Hyperbolic Systems
....................... 15
1.7
Notes on the One-Sided Exact Boundary Controllability and
Observability
........................................... 17
2
Semi-Global C1 Solutions for First Order
Quasilinear
Hyperbolic Systems
....................................... 19
2.1
Introduction
............................................ 19
2.2
Equivalence of Problem I and Problem II
................... 21
2.3
Local C1 Solution to the Mixed Initial-Boundary Value
Problem
................................................ 27
2.4
Semi-Global C1 Solution to the Mixed Initial-Boundary
Value Problem
.......................................... 27
2.5
Remarks
............................................... 33
3
Exact Controllability for First Order
Quasilinear
Hyperbolic Systems
....................................... 37
3.1
Introduction and Main Results
............................ 37
3.2
Framework of Resolution
................................. 41
3.3
Two-Sided Control—Proof of Theorem
3.1................... 42
3.4
One-Sided Control—Proof of Theorem
3.2.................. 47
3.5
Two-Sided Control with Less Controls
—
Proof of Theorem
3.3. 52
VIII Contents
3.6
Exact
Controllability for First Order
Quasilinear
Hyperbolic
Systems with Zero Eigenvalues
............................ 57
4
Exact Observability for First Order
Quasilinear
Hyperbolic Systems
....................................... 63
4.1
Introduction and Main Results
............................ 63
4.2
Two-Sided Observation—Proof of Theorem
4.1.............. 67
4.3
One-Sided Observation—Proof of Theorem
4.2.............. 70
4.4
Two-Sided Observation with Less Observed Values
—
Proof of
Theorem
4.3............................................ 71
4.5
Exact Observability for First Order
Quasilinear
Hyperbolic
Systems with Zero Eigenvalues
............................ 73
4.6
Duality Between Controllability and Observability for First
Order
Quasilinear
Hyperbolic Systems
..................... 74
5
Exact Boundary Controllability for
Quasilinear
Wave
Equations
.................................................. 77
5.1
Introduction and Main Results
............................ 77
5.2
Semi-Global C2 Solution for 1-D
Quasilinear
Wave Equations
. 80
5.3
Two-Sided Control
—
Proof of Theorem
5.1.................. 83
5.4
One-Sided Control—Proof of Theorem
5.2.................. 88
5.5
Remarks
............................................... 90
6
Exact Boundary Observability for
Quasilinear
Wave
Equations
.................................................. 93
6.1
Introduction
............................................ 93
6.2
Semi-Global C2 Solution for 1-D
Quasilinear
Wave Equations
(Continued)
............................................ 94
6.3
Exact Boundary Observability
............................ 97
6.4
Duality Between Controllability and Observability for
Quasilinear
Wave Equations
..............................101
7
Exact Boundary Controllability of Unsteady Flows in a
Tree-Like Network of Open Canals
........................103
7.1
Introduction
............................................103
7.2
Preliminaries
............................................105
7.3
Exact Boundary Controllability of Unsteady Flows in a
Single Open Canal
.......................................107
7.4
Exact Boundary Controllability for
Quasilinear
Hyperbolic
Systems on a Star-Like Network
...........................112
7.5
Exact Boundary Controllability of Unsteady Flows in a
Star-Like Network of Open Canals
.........................119
7.6
Exact Boundary Controllability of Unsteady Flows in a
Tree-Like Network of Open Canals
.........................123
7.7
Remarks
...............................................127
Contents
IX
8
Exact Boundary Observability of Unsteady Flows in a
Tree-Like Network of Open Canals
........................129
8.1
Introduction
............................................129
8.2
Preliminaries
............................................130
8.3
Exact Boundary Observability of Unsteady Flows in a Single
Open Canal
............................................132
8.4
Exact Boundary Observability of Unsteady Flows in a
Star-Like Network of Open Canals
.........................136
8.5
Exact Boundary Observability of Unsteady Flows in a
Tree-Like Network of Open Canals
.........................148
8.6
Duality Between Controllability and Observability in a
Tree-Like Network of Open Canals
.........................154
9
Controllability and Observability for Nonautonomous
Hyperbolic Systems
.......................................155
9.1
Introduction
............................................155
9.2
Two-Sided Control
......................................156
9.3
One-Sided Control
.......................................161
9.4
Two-Sided Observation
...................................164
9.5
One-Sided Observation
...................................165
9.6
Remarks
...............................................167
10
Note on the One-Sided Exact Boundary Controllability
for First Order
Quasilinear
Hyperbolic Systems
...........171
10.1
Introduction
............................................171
10.2
Reduction of the Problem
................................174
10.3
Semi-Global C2 Solution to a Class of Second Order
Quasilinear Hyperbolic Equations
.........................177
10.4
One-Sided Exact Boundary Controllability for a Class of
Second Order Quasilinear Hyperbolic Equations
.............180
11
Note on the One-Sided Exact Boundary Observability for
First Order Quasilinear Hyperbolic Systems
...............185
11.1
Introduction
............................................185
11.2
Reduction of the Problem
................................188
11.3
Proof of Theorem
11.1...................................190
11.4
Duality Between Controllability and Observability
.........193
Appendix A: An Introduction to Quasilinear Hyperbolic
Systems
...................................................195
A.I Definition of Quasilinear Hyperbolic System
................195
A.
2
Characteristic Form of Hyperbolic System
..................198
A.3 Reducible Quasilinear Hyperbolic System. Riemann Invariants
199
A.4 Blow-Up Phenomenon
...................................201
A.5 Cauchy Problem
........................................202
X
Contents
Α.6
Mixed Initial-Boundary Value Problem
.....................203
A.
7
Decomposition of Waves
..................................205
References
.....................................................211
Index
..........................................................217
|
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| id | DE-604.BV036447089 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:33:37Z |
| institution | BVB |
| isbn | 9787040241631 7040241633 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020319317 |
| oclc_num | 705500929 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-29T DE-83 DE-11 |
| owner_facet | DE-703 DE-384 DE-29T DE-83 DE-11 |
| physical | X, 222 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Institute of Mathematical Sciences |
| record_format | marc |
| series | AIMS on applied mathematics |
| series2 | AIMS on applied mathematics |
| spellingShingle | Li, Daqian 1937- Controllability and observability for quasilinear hyperbolic systems AIMS on applied mathematics Quasilineare hyperbolische Differentialgleichung (DE-588)4651046-1 gnd Steuerbarkeit (DE-588)4134713-4 gnd |
| subject_GND | (DE-588)4651046-1 (DE-588)4134713-4 |
| title | Controllability and observability for quasilinear hyperbolic systems |
| title_auth | Controllability and observability for quasilinear hyperbolic systems |
| title_exact_search | Controllability and observability for quasilinear hyperbolic systems |
| title_full | Controllability and observability for quasilinear hyperbolic systems Tatsien Li |
| title_fullStr | Controllability and observability for quasilinear hyperbolic systems Tatsien Li |
| title_full_unstemmed | Controllability and observability for quasilinear hyperbolic systems Tatsien Li |
| title_short | Controllability and observability for quasilinear hyperbolic systems |
| title_sort | controllability and observability for quasilinear hyperbolic systems |
| topic | Quasilineare hyperbolische Differentialgleichung (DE-588)4651046-1 gnd Steuerbarkeit (DE-588)4134713-4 gnd |
| topic_facet | Quasilineare hyperbolische Differentialgleichung Steuerbarkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020319317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023094684 |
| work_keys_str_mv | AT lidaqian controllabilityandobservabilityforquasilinearhyperbolicsystems |