Scaling limits and models in physical processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
1998
|
| Series: | Deutsche Mathematiker-Vereinigung: DMV-Seminar
28 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008200008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | VI, 190 S. graph. Darst. |
| ISBN: | 3764359854 0817659854 |
Staff View
MARC
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| 245 | 1 | 0 | |a Scaling limits and models in physical processes |c Carlo Cercignani ; David H. Sattinger |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 1998 | |
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Record in the Search Index
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| adam_text | Contents
I Scaling and Mathematical Models in Kinetic Theory
Preface 3
1 Boltzmann Equation and Gas Surface Interaction
1.1 Introduction 5
1.2 The Boltzmann equation 6
1.3 Molecules different from hard spheres 11
1.4 Collision invariants 13
1.5 The Boltzmann inequality and the Maxwell distributions 16
1.6 The macroscopic balance equations 17
1.7 The H theorem 22
1.8 Equilibrium states and Maxwellian distributions 24
1.9 Model equations 25
1.10 Boundary conditions 28
Bibliography 34
2 Perturbation Methods for the Boltzmann Equation
2.1 Introduction 37
2.2 Rarefaction regimes 39
2.3 Solving the Boltzmann equation. Analytical techniques 40
2.4 Hydrodynamical limit and other scalings 44
2.5 The linearized collision operator 46
2.6 The basic properties of the linearized collision operat or 48
2.7 Spectral properties of the Fourier transformed, linearized
Boltzmann equation 54
2.8 The asymptotic behavior of the solution of the Cauchy problem
for the linearized Boltzmann equation 58
2.9 A quick survey of the global existence theorems for
the nonlinear equation 60
2.10 Hydrodynamical limits. A formal discussion 63
2.11 The Hilbert expansion 66
2.12 The entropy approach to the hydrodynamical limit 68
2.13 The hydrodynamic limit for short times 72
2.14 Other scalings and the incompressible Navier Stokes equations . . 74
2.15 Concluding remarks 78
Bibliography 80
Index 83
vi Contents
II Scaling, Mathematical Modelling, Integrable Systems
Preface 89
1 Dispersion
1.1 Introduction 91
1.2 Group and phase velocities 92
2 Nonlinear Schrodinger Equation
2.1 Multiple scales expansion 101
2.2 Pulse solutions 104
3 Korteweg de Vries
3.1 Background and history 107
3.2 Plasmas 111
3.3 Water waves 114
3.4 The solitary wave of the KdV equation 120
4 Isospeetral Deformations
4.1 The KdV hierarchy 123
4.2 The AKNS hierarchy 127
5 Inverse Scattering Theory
5.1 The Schrodinger equation 131
5.2 First Order Systems 142
5.3 Decay of the scattering data 150
6 Variational Methods
6.1 Water Waves 153
6.2 Method of Averaging 155
7 Weak and Strong Nonlinearities
7.1 Breaking and Peaking 161
7.2 Strongly nonlinear models 164
7.3 The extended AKNS hierarchy 170
8 Numerical Methods
8.1 The finite Fourier transform 175
8.2 Pseudospectral codes 182
Bibliography 186
Index 191
|
| any_adam_object | 1 |
| author | Cercignani, Carlo 1939-2010 Sattinger, David H. |
| author_GND | (DE-588)132954184 |
| author_facet | Cercignani, Carlo 1939-2010 Sattinger, David H. |
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| author_sort | Cercignani, Carlo 1939-2010 |
| author_variant | c c cc d h s dh dhs |
| building | Verbundindex |
| bvnumber | BV012110236 |
| classification_rvk | SK 540 SK 950 UX 1200 |
| classification_tum | PHY 050f |
| ctrlnum | (OCoLC)247454712 (DE-599)BVBBV012110236 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012110236 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:24:30Z |
| institution | BVB |
| isbn | 3764359854 0817659854 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008200008 |
| oclc_num | 247454712 |
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| owner | DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 |
| physical | VI, 190 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Deutsche Mathematiker-Vereinigung: DMV-Seminar |
| series2 | Deutsche Mathematiker-Vereinigung: DMV-Seminar |
| spellingShingle | Cercignani, Carlo 1939-2010 Sattinger, David H. Scaling limits and models in physical processes Deutsche Mathematiker-Vereinigung: DMV-Seminar Integrables System (DE-588)4114032-1 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4163881-5 (DE-588)4205012-1 (DE-588)4128900-6 |
| title | Scaling limits and models in physical processes |
| title_auth | Scaling limits and models in physical processes |
| title_exact_search | Scaling limits and models in physical processes |
| title_full | Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger |
| title_fullStr | Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger |
| title_full_unstemmed | Scaling limits and models in physical processes Carlo Cercignani ; David H. Sattinger |
| title_short | Scaling limits and models in physical processes |
| title_sort | scaling limits and models in physical processes |
| topic | Integrables System (DE-588)4114032-1 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Integrables System Kinetische Gastheorie Skalierungsgesetz Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008200008&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000020322 |
| work_keys_str_mv | AT cercignanicarlo scalinglimitsandmodelsinphysicalprocesses AT sattingerdavidh scalinglimitsandmodelsinphysicalprocesses |
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Branch Library Mathematics & Informatics
| Call Number: |
0102 MAT 001f 2001 A 1046-28
Floor plan |
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| Copy 1 | Available for loan On Shelf |