The Cauchy problem for higher order abstract differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Lecture notes in mathematics
1701 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 300 S. |
| ISBN: | 3540652388 |
Internformat
MARC
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| 100 | 1 | |a Xiao, Ti-Jun |d 1964- |e Verfasser |0 (DE-588)120518228 |4 aut | |
| 245 | 1 | 0 | |a The Cauchy problem for higher order abstract differential equations |c Ti-Jun Xiao and Jin Liang |
| 246 | 1 | 3 | |a The Cauchy problem for higher-order abstract differential equations |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XII, 300 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1701 | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Cauchy problem | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Hilbert space | |
| 650 | 0 | 7 | |a Abstrakte Differentialgleichung |0 (DE-588)4141144-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ordnung n |0 (DE-588)4322729-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Abstrakte Differentialgleichung |0 (DE-588)4141144-4 |D s |
| 689 | 0 | 1 | |a Ordnung n |0 (DE-588)4322729-6 |D s |
| 689 | 0 | 2 | |a Cauchy-Anfangswertproblem |0 (DE-588)4147404-1 |D s |
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| 700 | 1 | |a Liang, Jin |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804126829563346944 |
|---|---|
| adam_text | Contents
Chapter 1. Laplace transforms and operator families in locally convex spaces
Summary 1
1.1 Laplace transforms 2
1.2 An integrated version of Widder s theorem in SCLCS 8
1.3 Integrated, regularized semigroups 12
1.4 Integrated, regularized cosine functions 18
1.5 Differential operators as generators 19
1.6 Relationship to Cauchy problems 35
1.7 Notes 42
Chapter 2. Wellposedness and solvability
Summary 45
2.1 Basic properties 46
2.2 Strong wellposedness 54
2.3 Solvability 67
2.4 Perturbation 68
2.5 Two typical cases 74
2.6 Notes 78
Chapter 3. Generalized wellposedness
Summary 85
3.1 Criteria for general (ACPn) 86
3.2 The special case (I): coefficient operators relating to integrated
semigroups 91
3.3 The special case (II): coefficient operators relating to integrated
semigroups (continuation) 99
3.4 The special case (III): coefficient operators relating to integrated
cosine functions Ill
3.5 C wellposedness 115
3.6 The case « )(*) = Au(t) 130
3.7 Notes 139
XII Contents
Chapter 4. Analyticity and parabolicity
Summary 141
4.1 Analyticity 142
4.2 Parabolicity 150
4.3 The case of differential operators as coefficient operators 160
4.4 Entire solutions 167
4.5 Notes 176
Chapter 5. Exponential growth bound and exponential stability
Summary 177
5.1 Exponential growth bound of the propagators 177
5.2 Exponential stability of solutions 188
5.3 Notes 196
Chapter 6. Differentiability and norm continuity
Summary 199
6.1 Differentiability 199
6.2 Norm continuity (general case) 214
6.3 Norm continuity (a special case) 221
6.4 Operator matrices generating various semigroups 225
6.5 Notes 237
Chapter 7. Almost periodicity
Summary 239
7.1 Incomplete second order equations 239
7.2 Complete second order equations 249
7.3 Notes 261
Appendix 263
Al Fractional powers of nonnegative operators 263
A2 Strongly continuous semigroups and cosine functions 264
Bibliography 269
Index 299
Symbols 301
|
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| id | DE-604.BV012211193 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:23:40Z |
| institution | BVB |
| isbn | 3540652388 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008275622 |
| oclc_num | 889821527 |
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| physical | XII, 300 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Xiao, Ti-Jun 1964- Verfasser (DE-588)120518228 aut The Cauchy problem for higher order abstract differential equations Ti-Jun Xiao and Jin Liang The Cauchy problem for higher-order abstract differential equations Berlin [u.a.] Springer 1998 XII, 300 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1701 Banach spaces Cauchy problem Differential equations Hilbert space Abstrakte Differentialgleichung (DE-588)4141144-4 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Abstrakte Differentialgleichung (DE-588)4141144-4 s Ordnung n (DE-588)4322729-6 s Cauchy-Anfangswertproblem (DE-588)4147404-1 s DE-604 Liang, Jin Verfasser aut Lecture notes in mathematics 1701 (DE-604)BV000676446 1701 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008275622&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xiao, Ti-Jun 1964- Liang, Jin The Cauchy problem for higher order abstract differential equations Lecture notes in mathematics Banach spaces Cauchy problem Differential equations Hilbert space Abstrakte Differentialgleichung (DE-588)4141144-4 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Ordnung n (DE-588)4322729-6 gnd |
| subject_GND | (DE-588)4141144-4 (DE-588)4147404-1 (DE-588)4322729-6 |
| title | The Cauchy problem for higher order abstract differential equations |
| title_alt | The Cauchy problem for higher-order abstract differential equations |
| title_auth | The Cauchy problem for higher order abstract differential equations |
| title_exact_search | The Cauchy problem for higher order abstract differential equations |
| title_full | The Cauchy problem for higher order abstract differential equations Ti-Jun Xiao and Jin Liang |
| title_fullStr | The Cauchy problem for higher order abstract differential equations Ti-Jun Xiao and Jin Liang |
| title_full_unstemmed | The Cauchy problem for higher order abstract differential equations Ti-Jun Xiao and Jin Liang |
| title_short | The Cauchy problem for higher order abstract differential equations |
| title_sort | the cauchy problem for higher order abstract differential equations |
| topic | Banach spaces Cauchy problem Differential equations Hilbert space Abstrakte Differentialgleichung (DE-588)4141144-4 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Ordnung n (DE-588)4322729-6 gnd |
| topic_facet | Banach spaces Cauchy problem Differential equations Hilbert space Abstrakte Differentialgleichung Cauchy-Anfangswertproblem Ordnung n |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008275622&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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