Evolution equations in scales of banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart [u.a.]
Teubner
2002
|
| Edition: | 1. Aufl. |
| Series: | Teubner-Texte zur Mathematik ; 140
140 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [295] - 306 |
| Physical Description: | 309 S. Ill. |
| ISBN: | 3519003767 |
Staff View
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| 245 | 1 | 0 | |a Evolution equations in scales of banach spaces |c Oliver Caps |
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 140 | |
| 500 | |a Literaturverz. S. [295] - 306 | ||
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Record in the Search Index
| _version_ | 1804136150063906816 |
|---|---|
| adam_text | Contents
List of Symbols 9
Conventions 12
Introduction 13
1 Tools from functional analysis 27
1.1 A brief introduction into the theory of semigroups 27
1.2 Selfadjoint operators 38
1.3 Generators of analytic semigroups and their powers 45
1.4 Fractional Powers of operators of positive type 53
1.5 Complex interpolation spaces 59
1.6 Time dependent, linear evolution equations 66
2 Well posedness of the time dependent linear Cauchy problem 78
2.1 Properties of well posed linear Cauchy problems in scales of Ba
nach spaces 79
2.2 Scales of Banach spaces generated by families of closed operators 89
2.3 Commutator estimates and scales of Banach spaces 100
2.4 Characterization of well posedness of the Cauchy problem . . . 109
2.5 Sufficient conditions for well posedness of the Cauchy problem . 113
3 Quasilinear Evolution Equations 130
3.1 Semilinear Evolution Equations 130
3.2 Commutator estimates and quasilinear evolution equations . . 140
3.3 A local existence and uniqueness result for quasilinear evolution
equations 147
3.4 Regularity for quasilinear evolution equations in scales of Ba¬
nach spaces 162
4 Applications to linear, time dependent evolution equations 166
4.1 Pseudodifferential operators and weighted Sobolev spaces . . . 167
4.2 Pseudodifferential evolution equations in scales of weighted
Sobolev spaces 186
4.3 Essential selfadjointness of pseudodifferential operators 199
8 Contents
4.4 Evolution equations in C0(Rn) and Feller semigroups 212
4.5 Evolution equations in scales of L9 Sobolev spaces 221
4.6 An application to a degenerate elliptic boundary value problem 227
4.7 Evolution equations on networks 234
5 Applications to quasilinear evolution equations 245
5.1 Estimates of Nash Moser type for differential operators 246
5.2 Quasilinear evolution equations in Sobolev spaces 265
5.3 Degenerate Navier Stokes equations 271
5.4 The generalized Kadomtsev Petviashvili equation 278
5.5 Quasilinear evolution equations in scales of L9 Sobolev spaces . 290
5.6 First order hyperbolic evolution equations in the Co scale . . . 292
Bibliography 295
Index 307
|
| adam_txt |
Contents
List of Symbols 9
Conventions 12
Introduction 13
1 Tools from functional analysis 27
1.1 A brief introduction into the theory of semigroups 27
1.2 Selfadjoint operators 38
1.3 Generators of analytic semigroups and their powers 45
1.4 Fractional Powers of operators of positive type 53
1.5 Complex interpolation spaces 59
1.6 Time dependent, linear evolution equations 66
2 Well posedness of the time dependent linear Cauchy problem 78
2.1 Properties of well posed linear Cauchy problems in scales of Ba
nach spaces 79
2.2 Scales of Banach spaces generated by families of closed operators 89
2.3 Commutator estimates and scales of Banach spaces 100
2.4 Characterization of well posedness of the Cauchy problem . . . 109
2.5 Sufficient conditions for well posedness of the Cauchy problem . 113
3 Quasilinear Evolution Equations 130
3.1 Semilinear Evolution Equations 130
3.2 Commutator estimates and quasilinear evolution equations . . 140
3.3 A local existence and uniqueness result for quasilinear evolution
equations 147
3.4 Regularity for quasilinear evolution equations in scales of Ba¬
nach spaces 162
4 Applications to linear, time dependent evolution equations 166
4.1 Pseudodifferential operators and weighted Sobolev spaces . . . 167
4.2 Pseudodifferential evolution equations in scales of weighted
Sobolev spaces 186
4.3 Essential selfadjointness of pseudodifferential operators 199
8 Contents
4.4 Evolution equations in C0(Rn) and Feller semigroups 212
4.5 Evolution equations in scales of L9 Sobolev spaces 221
4.6 An application to a degenerate elliptic boundary value problem 227
4.7 Evolution equations on networks 234
5 Applications to quasilinear evolution equations 245
5.1 Estimates of Nash Moser type for differential operators 246
5.2 Quasilinear evolution equations in Sobolev spaces 265
5.3 Degenerate Navier Stokes equations 271
5.4 The generalized Kadomtsev Petviashvili equation 278
5.5 Quasilinear evolution equations in scales of L9 Sobolev spaces . 290
5.6 First order hyperbolic evolution equations in the Co scale . . . 292
Bibliography 295
Index 307 |
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| author | Caps, Oliver |
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| classification_rvk | SK 560 SK 540 SK 600 |
| ctrlnum | (OCoLC)50779491 (DE-599)BVBBV022174871 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV022174871 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:20:07Z |
| indexdate | 2024-07-09T20:51:49Z |
| institution | BVB |
| isbn | 3519003767 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015389593 |
| oclc_num | 50779491 |
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| physical | 309 S. Ill. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik ; 140 |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Caps, Oliver Verfasser aut Evolution equations in scales of banach spaces Oliver Caps 1. Aufl. Stuttgart [u.a.] Teubner 2002 309 S. Ill. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 140 Literaturverz. S. [295] - 306 Banach spaces Evolution equations Banach-Raum (DE-588)4004402-6 gnd rswk-swf Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Banach-Raum (DE-588)4004402-6 s DE-604 Evolutionsgleichung (DE-588)4129061-6 s Cauchy-Anfangswertproblem (DE-588)4147404-1 s Teubner-Texte zur Mathematik ; 140 140 (DE-604)BV000012607 140 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015389593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Caps, Oliver Evolution equations in scales of banach spaces Teubner-Texte zur Mathematik ; 140 Banach spaces Evolution equations Banach-Raum (DE-588)4004402-6 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4147404-1 (DE-588)4129061-6 (DE-588)4123623-3 |
| title | Evolution equations in scales of banach spaces |
| title_auth | Evolution equations in scales of banach spaces |
| title_exact_search | Evolution equations in scales of banach spaces |
| title_exact_search_txtP | Evolution equations in scales of banach spaces |
| title_full | Evolution equations in scales of banach spaces Oliver Caps |
| title_fullStr | Evolution equations in scales of banach spaces Oliver Caps |
| title_full_unstemmed | Evolution equations in scales of banach spaces Oliver Caps |
| title_short | Evolution equations in scales of banach spaces |
| title_sort | evolution equations in scales of banach spaces |
| topic | Banach spaces Evolution equations Banach-Raum (DE-588)4004402-6 gnd Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Banach spaces Evolution equations Banach-Raum Cauchy-Anfangswertproblem Evolutionsgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015389593&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT capsoliver evolutionequationsinscalesofbanachspaces |