Optimal control of partial differential equations: theory, methods, and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Providence, RI
American Mathematical Sociecty
2010
|
| Series: | Graduate studies in mathematics
112 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 399 Seiten Illustrationen |
| ISBN: | 9780821849040 |
Staff View
MARC
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| 100 | 1 | |a Tröltzsch, Fredi |d 1951- |0 (DE-588)109612949 |4 aut | |
| 240 | 1 | 0 | |a Optimale Steuerung partieller Differentialgleichungen |
| 245 | 1 | 0 | |a Optimal control of partial differential equations |b theory, methods, and applications |c Fredi Tröltzsch |
| 264 | 1 | |a Providence, RI |b American Mathematical Sociecty |c 2010 | |
| 300 | |a XV, 399 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 112 | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
| _version_ | 1804140851563069440 |
|---|---|
| adam_text | Contents
Preface
to the English edition
xi
Preface to the German edition
xiii
Chapter
1.
Introduction and examples
1
§1.1.
What is optimal control?
1
§1.2.
Examples of convex problems
3
§1.3.
Examples of nonconvex problems
7
§1.4.
Basic concepts for the finite-dimensional case
9
Chapter
2.
Linear-quadratic elliptic control problems
21
§2.1.
Normed spaces
21
§2.2.
Sobolev spaces
24
§2.3.
Weak solutions to elliptic equations
30
§2.4.
Linear mappings
40
§2.5.
Existence of optimal controls
48
§2.6.
Differentiability in Banach spaces
56
§2.7.
Adjoint operators
60
§2.8.
First-order necessary optimality conditions
63
§2.9.
Construction of test examples
80
§2.10.
The formal
Lagrange
method
84
§2.11.
Further examples
* 89
§2.12.
Numerical methods
91
§2.13.
The adjoint state as
a
Lagrange
multiplier
* 106
§2.14.
Higher regularity for elliptic problems 111
§2.15.
Regularity of optimal controls
114
vii
viii Contents
§2.16.
Exercises
116
Chapter
3.
Linear-quadratic parabolic control problems
119
§3.1.
Introduction
119
§3.2.
Fourier s method in the spatially one-dimensional case
124
§3.3.
Weak solutions in
W¡ °{Q)
136
§3.4.
Weak solutions in W(0, T)
141
§3.5.
Parabolic optimal control problems
153
§3.6.
Necessary optimality conditions
156
§3.7.
Numerical methods
166
§3.8.
Derivation of Fourier expansions
171
§3.9.
Linear continuous functionals as right-hand sides
* 175
§3.10.
Exercises
177
Chapter
4.
Optimal control of semilinear elliptic equations
181
§4.1.
Preliminary remarks
181
§4.2.
A semilinear elliptic model problem
182
§4.3.
Nemytskii operators
196
§4.4.
Existence of optimal controls
205
§4.5.
The control-to-state operator
211
§4.6.
Necessary optimality conditions
215
§4.7.
Application of the formal
Lagrange
method
220
§4.8.
Pontryagin s maximum principle
* 224
§4.9.
Second-order derivatives
226
§4.10.
Second-order optimality conditions
231
§4.11.
Numerical methods
257
§4.12.
Exercises
263
Chapter
5.
Optimal control of semilinear parabolic equations
265
§5.1.
The semilinear parabolic model problem
265
§5.2.
Basic assumptions for the chapter
268
§5.3.
Existence of optimal controls
270
§5.4.
The control-to-state operator
273
§5.5.
Necessary optimality conditions
277
§5.6.
Pontryagin s maximum principle
* 285
§5.7.
Second-order optimality conditions
286
§5.8.
Test examples
298
Contents ix
§5.9.
Numerical methods
308
§5.10.
Further parabolic problems
* 313
§5.11.
Exercises
321
Chapter
6.
Optimization problems in Banach spaces
323
§6.1.
The Karush-Kuhn-Tucker conditions
323
§6.2.
Control problems with state constraints
338
§6.3.
Exercises
353
Chapter
7.
Supplementary results on partial differential equations
355
§7.1.
Embedding results
355
§7.2.
Elliptic equations
356
§7.3.
Parabolic problems
366
Bibliography
385
Index
397
|
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| dewey-raw | 515/.642 |
| dewey-search | 515/.642 |
| dewey-sort | 3515 3642 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035875125 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:33Z |
| institution | BVB |
| isbn | 9780821849040 |
| language | English German |
| lccn | 2009037756 |
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| physical | XV, 399 Seiten Illustrationen |
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| publisher | American Mathematical Sociecty |
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| series | Graduate studies in mathematics |
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| spelling | Tröltzsch, Fredi 1951- (DE-588)109612949 aut Optimale Steuerung partieller Differentialgleichungen Optimal control of partial differential equations theory, methods, and applications Fredi Tröltzsch Providence, RI American Mathematical Sociecty 2010 XV, 399 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 112 Control theory Differential equations, Partial Mathematical optimization Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Optimale Kontrolle (DE-588)4121428-6 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1174-9 Graduate studies in mathematics 112 (DE-604)BV009739289 112 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tröltzsch, Fredi 1951- Optimal control of partial differential equations theory, methods, and applications Graduate studies in mathematics Control theory Differential equations, Partial Mathematical optimization Partielle Differentialgleichung (DE-588)4044779-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4121428-6 (DE-588)4123623-3 |
| title | Optimal control of partial differential equations theory, methods, and applications |
| title_alt | Optimale Steuerung partieller Differentialgleichungen |
| title_auth | Optimal control of partial differential equations theory, methods, and applications |
| title_exact_search | Optimal control of partial differential equations theory, methods, and applications |
| title_full | Optimal control of partial differential equations theory, methods, and applications Fredi Tröltzsch |
| title_fullStr | Optimal control of partial differential equations theory, methods, and applications Fredi Tröltzsch |
| title_full_unstemmed | Optimal control of partial differential equations theory, methods, and applications Fredi Tröltzsch |
| title_short | Optimal control of partial differential equations |
| title_sort | optimal control of partial differential equations theory methods and applications |
| title_sub | theory, methods, and applications |
| topic | Control theory Differential equations, Partial Mathematical optimization Partielle Differentialgleichung (DE-588)4044779-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Control theory Differential equations, Partial Mathematical optimization Partielle Differentialgleichung Optimale Kontrolle Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT troltzschfredi optimalesteuerungpartiellerdifferentialgleichungen AT troltzschfredi optimalcontrolofpartialdifferentialequationstheorymethodsandapplications |