Models of phase transitions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1996
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 322 S. graph. Darst. |
| ISBN: | 3764337680 0817637680 |
Internformat
MARC
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| 100 | 1 | |a Visintin, Augusto |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Models of phase transitions |c Augusto Visintin |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a VII, 322 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 28 | |
| 650 | 7 | |a Equations aux dérivés partielles - Solutions numériques |2 ram | |
| 650 | 7 | |a Transitions de phases - Modèles mathématiques |2 ram | |
| 650 | 7 | |a Transport, Théorie du - Modèles mathématiques |2 ram | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Phase transformations (Statistical physics) |x Mathematical models | |
| 650 | 4 | |a Transport theory |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1804125730870657024 |
|---|---|
| adam_text | Contents
Preface ix
Introduction 1
Reader s Guide 4
Part 1. Some Nonlinear P.D.E.S
Prelude 5
I. Models and P.D.E.s 6
1. Modelling and Analysis 6
2. Nonlinear P.D.E.s and Minimization Problems 12
3. Examples of Nonlinear P.D.E.s 25
4. Comments 30
II. A Class of Quasilinear Parabolic P.D.E.s 31
1. Variational Techniques of L2 Type 31
2. Further Results via L2 Techniques 39
3. Techniques of L1 and L°° Type 47
4. Local Regularity Results 54
5. Integra] Transformations 58
6. Semigroup Techniques 61
7. Comments 65
III. Doubly Nonlinear Parabolic P.D.E.s 68
1. Doubly Nonlinear Parabolic Equations of First Type 68
2. Doubly Nonlinear Parabolic Equations of Second Type 74
3. Other Nonlinear Parabolic Equations 78
4. Use of Compactness by Strict Convexity 82
5. Comments 87
Part 2. Phase Transitions
IV. The Stefan Problem 90
1. Strong Formulation of the Stefan Problem 90
2. Surface Tension 96
3. Length Scales and Mushy Region 98
4. Weak Formulation of the Stefan Problem 100
vi Contents
5. On the Analysis of the Stefan Problem 104
6. Comparison between Strong and Weak Formulations 106
7. The Muskat and Hele Shaw Problems 110
8. A Stefan Type Problem Arising in Ferromagnetism 113
9. On the History of the Stefan Problem 117
10. Comments 121
V. Generalizations of the Stefan Problem 123
1. Kinetic Undercooling and Phase Relaxation 123
2. Phase Transition in Two Component Systems 131
3. Approach via Nonequilibrium Thermodynamics 137
4. Analysis of the Model of Section V.3 141
5. General Nonequilibrium Thermodynamics 143
6. The Evolution of the Free Energy 147
7. Comments 152
VI. The Gibbs Thomson Law 155
1. Free Energy 155
2. Entropy 160
3. Phase Dependent Conductivity 165
4. The Gibbs Thomson Law 167
5. The Phase Field Model 174
6. Comments 176
VII. Nucleation and Growth 178
1. Local and Global Minimizers 178
2. Nucleation 181
3. Stable and Metastable States 185
4. Pure Phases 187
5. From Nucleation to Growth 190
6. Mean Curvature Flow 193
7. Nonlinear Mean Curvature Flow 196
8. Hysteresis in Front Motion 198
9. Comments 200
VIII. The Stefan Gibbs Thomson Problem with Nucleation .... 203
1. Modes of Phase Transition 203
2. Formulation of the Problem 208
3. Some Auxiliary Results 213
4. Existence Result 216
5. The Mullins Sekerka Problem 225
6. Comments 227
Contents vii
IX. Two Scale Models of Phase Transitions 229
1. Two Scale Stefan Problem and Nonadiabatic Nucleation 229
2. Another Model with Surface Tension 237
3. A Mean Field Model 239
4. Micromagnetics 242
5. Some Comparisons 244
6. Comments 247
Appendix
X. Compactness by Strict Convexity 248
1. Extremality and Compactness 248
2. Strictly Convex Functionals 252
3. Applications 255
4. Comments 259
XI. Toolbox 260
1. Some Function Spaces 260
2. Sobolev Spaces 264
3. Compactness 268
4. Convexity 273
5. Monotonicity 279
6. Accretiveness 285
7. Minimization 288
8. Geometric Measure Theory 290
9. Other Results 293
Book Selection 295
Bibliography 297
Index 319
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:13Z |
| institution | BVB |
| isbn | 3764337680 0817637680 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007536419 |
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| physical | VII, 322 S. graph. Darst. |
| publishDate | 1996 |
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| publisher | Birkhäuser |
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| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Visintin, Augusto Verfasser aut Models of phase transitions Augusto Visintin Boston [u.a.] Birkhäuser 1996 VII, 322 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 28 Equations aux dérivés partielles - Solutions numériques ram Transitions de phases - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques ram Mathematisches Modell Differential equations, Partial Numerical solutions Phase transformations (Statistical physics) Mathematical models Transport theory Mathematical models Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Progress in nonlinear differential equations and their applications 28 (DE-604)BV007934389 28 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007536419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Visintin, Augusto Models of phase transitions Progress in nonlinear differential equations and their applications Equations aux dérivés partielles - Solutions numériques ram Transitions de phases - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques ram Mathematisches Modell Differential equations, Partial Numerical solutions Phase transformations (Statistical physics) Mathematical models Transport theory Mathematical models Phasenumwandlung (DE-588)4132140-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4132140-6 (DE-588)4044779-0 |
| title | Models of phase transitions |
| title_auth | Models of phase transitions |
| title_exact_search | Models of phase transitions |
| title_full | Models of phase transitions Augusto Visintin |
| title_fullStr | Models of phase transitions Augusto Visintin |
| title_full_unstemmed | Models of phase transitions Augusto Visintin |
| title_short | Models of phase transitions |
| title_sort | models of phase transitions |
| topic | Equations aux dérivés partielles - Solutions numériques ram Transitions de phases - Modèles mathématiques ram Transport, Théorie du - Modèles mathématiques ram Mathematisches Modell Differential equations, Partial Numerical solutions Phase transformations (Statistical physics) Mathematical models Transport theory Mathematical models Phasenumwandlung (DE-588)4132140-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Equations aux dérivés partielles - Solutions numériques Transitions de phases - Modèles mathématiques Transport, Théorie du - Modèles mathématiques Mathematisches Modell Differential equations, Partial Numerical solutions Phase transformations (Statistical physics) Mathematical models Transport theory Mathematical models Phasenumwandlung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007536419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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