Moving interfaces and quasilinear parabolic evolution equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Switzerland
Birkhäuser
[2016]
|
| Schriftenreihe: | Monographs in mathematics
Vol. 105 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 609 Seiten Illustrationen |
| ISBN: | 9783319276977 |
Internformat
MARC
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| 020 | |a 9783319276977 |c hbk |9 978-3-319-27697-7 | ||
| 035 | |a (OCoLC)953979052 | ||
| 035 | |a (DE-599)BVBBV043677049 | ||
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| 100 | 1 | |a Prüss, Jan |d 1951-2018 |e Verfasser |0 (DE-588)113443625 |4 aut | |
| 245 | 1 | 0 | |a Moving interfaces and quasilinear parabolic evolution equations |c Jan Prüss, Gieri Simonett |
| 264 | 1 | |a Switzerland |b Birkhäuser |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xix, 609 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs in mathematics |v Vol. 105 | |
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| 650 | 0 | 7 | |a Nichtlineare Evolutionsgleichung |0 (DE-588)4221363-0 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Monographs in mathematics |v Vol. 105 |w (DE-604)BV000008284 |9 105 | |
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Datensatz im Suchindex
| _version_ | 1804176441685835776 |
|---|---|
| adam_text | Contents
Preface ............................................................... v
Basic Notations....................................................... xv
General References................................................... xix
I Background 1
1 Problems and Strategies 3
1.1 Modeling ....................................................... 3
1.2 Entropy and Equilibria......................................... 14
1.3 Goals and Strategies........................................... 25
2 Tools from Differential Geometry
2.1 Differential Geometry of Hypersurfaces
2.2 Parameterized Hypersurfaces..........
2.3 Approximation of Hvpersurfaces . . .
2.4 The Manifold of Hypersurfaces in Rn .
2.5 Moving Hypersurfaces and Domains .
43
44
55
65
73
75
II Abstract Theory
87
3 Operator Theory and Semigroups 89
3.1 Sectorial Operators............................................... 89
3.2 The Derivation Operator...........................................101
3.3 Analytic Semigroups and Fractional Powers.........................110
3.4 Trace Spaces: Reai Interpolation..................................120
3.5 Maximal Regularity .............................................139
4 Vector-Valued Harmonic Analysis 149
4.1 7^-Boundedness..................................................149
4.2 Unconditionallity...............................................156
4.3 Operator-Valued Fourier Multipliers.............................164
XI
Contents
xii
4.4 7^-Sectoriality................................................174
4.5 Operators with 7Z-Bounded Functional Calculus..................182
5 Quasilinear Parabolic Evolution Equations 195
5.1 Local Well-Posedness...........................................195
5.2 Regularity.....................................................200
5.3 Normally Stable Equilibria ....................................202
5.4 Instability of Equilibria......................................210
5.5 Normally Hyperbolic Equilibria.................................213
5.6 The Stable and Unstable Foliations ............................220
5.7 Compactness and Long-Time Behaviour............................227
III Linear Theory 231
6 Elliptic and Parabolic Problems 233
6.1 Elliptic and Parabolic Problems on ln..........................233
6.2 Elliptic and Parabolic Systems on R+ ..........................249
6.3 General Domains................................................272
6.4 Elliptic and Parabolic Problems on Hypersurfaces...............283
6.5 Transmission Problems..........................................287
6.6 Linearized Stefan Problems.....................................293
6.7 The Linearized Verigin Problem.................................303
7 Generalized Stokes Problems 311
7.1 The Generalized Stokes Problem on Mn ...........................311
7.2 Generalized Stokes Problems in a Half-Space....................322
7.3 General Domains................................................337
7.4 Boundary Value Problems for the Laplacian......................351
8 Two-Phase Stokes Problems 363
8.1 Two-Phase Stokes Problems......................................363
8.2 Proof of Theorem 8.1.2.........................................371
8.3 The Model Problem: Harmonic Analysis...........................383
8.4 Asymmetric Two-Phase Stokes Problems...........................395
8.5 Proof of Theorem 8.4.1.........................................400
8.6 The Asymmetric Model Problem...................................406
IV Nonlinear Problems 417
9 Local Well-Posedness and Regularity 419
9.1 Reformulation on the Fixed Domain..............................419
9.2 The Fixed Point Argument.......................................434
9.3 Dependence on the Data.........................................435
Contents xiii
9.4 Regularity: The Parameter Trick....................................435
9.5 Estimates for the Nonlinearities...................................441
10 Linear Stability of Equilibria 451
10.1 Linearization at Equilibria.......................................451
10.2 The Spectrum of the Laplace-Beltrami Operator.....................459
10.3 Nontrivial Eigenvalues............................................460
10.4 Eigenvalue Zero...................................................463
10.5 Unstable Eigenvalues: Problems 1 and 3............................466
10.6 Unstable Eigenvalues: Problem 5...................................473
10.7 Unstable Eigenvalues: Problem 4...................................477
10.8 Unstable Eigenvalues: Problem 6...................................483
11 Qualitative Behaviour of the Semiflows 491
11.1 The Local Semiflows...............................................491
11.2 Tangent Spaces at Equilibria......................................494
11.3 Nonlinear Stability of Equilibria ................................504
11.4 Global Existence and Convergence..................................512
12 Further Parabolic Evolution Problems 515
12.1 Generalized Newtonian Flows.......................................515
12.2 Nematic Liquid Crystal Flows......................................521
12.3 Maxwell-Stefan Diffusion with Reactions...........................527
12.4 Stefan Problems with Surface Heat Capacity .......................542
12.5 Geometric Evolution Equations.....................................557
Biographical Comments..................................................571
Outlook and Future Challenges..........................................585
List of Figures .......................................................587
Bibliography...........................................................589
List of Symbols........................................................605
Subject Index..........................................................606
|
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| author | Prüss, Jan 1951-2018 Simonett, Gieri 1959- |
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| classification_rvk | SK 540 SK 560 |
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| discipline | Mathematik |
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| id | DE-604.BV043677049 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:32:14Z |
| institution | BVB |
| isbn | 9783319276977 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029090039 |
| oclc_num | 953979052 |
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| owner_facet | DE-188 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-384 DE-29T DE-706 |
| physical | xix, 609 Seiten Illustrationen |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Prüss, Jan 1951-2018 Verfasser (DE-588)113443625 aut Moving interfaces and quasilinear parabolic evolution equations Jan Prüss, Gieri Simonett Switzerland Birkhäuser [2016] © 2016 xix, 609 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics Vol. 105 Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Parabolische Differentialgleichung (DE-588)4173245-5 s DE-604 Simonett, Gieri 1959- Verfasser (DE-588)172575818 aut Erscheint auch als 978-3-319-27698-4 Online-Ausgabe Monographs in mathematics Vol. 105 (DE-604)BV000008284 105 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029090039&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prüss, Jan 1951-2018 Simonett, Gieri 1959- Moving interfaces and quasilinear parabolic evolution equations Monographs in mathematics Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| subject_GND | (DE-588)4173245-5 (DE-588)4221363-0 |
| title | Moving interfaces and quasilinear parabolic evolution equations |
| title_auth | Moving interfaces and quasilinear parabolic evolution equations |
| title_exact_search | Moving interfaces and quasilinear parabolic evolution equations |
| title_full | Moving interfaces and quasilinear parabolic evolution equations Jan Prüss, Gieri Simonett |
| title_fullStr | Moving interfaces and quasilinear parabolic evolution equations Jan Prüss, Gieri Simonett |
| title_full_unstemmed | Moving interfaces and quasilinear parabolic evolution equations Jan Prüss, Gieri Simonett |
| title_short | Moving interfaces and quasilinear parabolic evolution equations |
| title_sort | moving interfaces and quasilinear parabolic evolution equations |
| topic | Parabolische Differentialgleichung (DE-588)4173245-5 gnd Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd |
| topic_facet | Parabolische Differentialgleichung Nichtlineare Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029090039&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008284 |
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