Non-linear wave propagation: with applications to physics and magnetohydrodynamics
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Press
1966
|
| Edition: | 2. print. |
| Series: | Mathematics in science and engineering
9 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 369 S. Ill., graph. Darst. |
Staff View
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| 245 | 1 | 0 | |a Non-linear wave propagation |b with applications to physics and magnetohydrodynamics |c A. Jeffrey ; T. Taniuti |
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| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1966 | |
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Record in the Search Index
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| adam_text | Contents
Preface v
PART I—GENERAL THEORY
Chapter I
General Hyperbolic Equations
1.1 The Wave and Hyperbolic Equations 3
1.2 The Cauchy Problem and Characteristics 9
1.3 Mixed Boundary and Initial Value Problems 15
1.4 Non Linear Equations, Quasi Linear Systems, and Lipschitz
Continuous Solutions 24
1.5 Systems of Quasi Linear Equations with Many Variables . . . 29
1.6 Quasi Linear Hyperbolic First Order Systems and Characteristics 33
1.7 Rays and Wave Fronts 40
1.8 Illustrative Examples: The Maxwell Equations 48
1.9 Hydrodynamics 57
Chapter 2
The Method of Characteristics
2.1 Riemann Invariants—Systems with Two Dependent Variables 65
2.2 Generalised Riemann Invariants—System with n Dependent
Variables 85
2.3 Mixed Boundary and Initial Value Problems 94
2.4 Propagation of Discontinuities along Wave Fronts 100
vii
Viii CONTENTS
Chapter 3
Conservation Laws and Weak Solutions
3.1 Conservation Laws Ill
3.2 Weak Solutions 116
3.3 Evolutionary Conditions on Discontinuities in Conservation
Laws of Hyperbolic Type 124
3.4 Evolutionary Conditions on a General System 125
3.5 General Shock Relations 130
3.6 Hydrodynamic Discontinuities 135
3.7 Numerical Solution of Non Linear Hyperbolic Systems . . . 141
3.8 The Propagation of Weak Discontinuities along Rays .... 149
3.9 Geometrical Acoustics—The Theory of Weak Shock Waves . . 159
PART II—THE APPLICATION TO
MAGNETOHYDRODYNAMICS
Chapter 4
The Fundamental Equations and Characteristics
4.1 Basic Equations and Assumptions 167
4.2 The Adiabatic Reversible System and the Lundquist Equations 170
4.3 The Characteristic Equations 171
4.4 Wave Front Diagram 177
4.5 Propagation of Weak Hydromagnetic Discontinuities . . . .189
Chapter 5
Simple Waves
5.1 Properties of Magnetic Lines of Force 195
5.2 Simple Waves in One Dimensional Propagation 202
CONTENTS IX
Chapter 6
Magnetohydrodynamic Shocks
6.1 The Conservation Laws 214
6.2 Fast and Slow Shocks 219
6.3 Limit Shocks 238
6.4 Transverse Shocks and Contact Discontinuities 249
Chapter 7
Interaction of Hydromagnetic Waves
7.1 Further Considerations on the Evolutionary Condition . . . 256
7.2 The Piston Problem 259
7.3 Riemann s Problem 276
Chapter 8
Spatial Discontinuities
8.1 Weak Discontinuities in Steady Flows 293
8.2 The Eeducible Form of Plane Aligned Field Flow 299
8.3 Oblique Shock Waves 311
8.4 The Discontinuity in the Static Case 317
Appendices
A. Basic Theorems in Matrix Theory 321
B. The Rankine Hugoniot Relation 327
C. The Behaviour of X? 331
D. Shock Relations 334
E. The Representation of the Hydromagnetic Equations .... 339
F. Contact Transformations and the Legendre Transformation . 347
References to Past I 357
References to Part TI 359
Index 363
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| any_adam_object | 1 |
| author | Jeffrey, Alan Taniuti, Tosiya |
| author_facet | Jeffrey, Alan Taniuti, Tosiya |
| author_role | aut aut |
| author_sort | Jeffrey, Alan |
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| building | Verbundindex |
| bvnumber | BV001930839 |
| classification_rvk | UR 8500 |
| ctrlnum | (OCoLC)256319304 (DE-599)BVBBV001930839 |
| discipline | Physik |
| edition | 2. print. |
| format | Book |
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| id | DE-604.BV001930839 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:26Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001258533 |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-20 DE-706 |
| physical | IX, 369 S. Ill., graph. Darst. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Acad. Press |
| record_format | marc |
| series | Mathematics in science and engineering |
| series2 | Mathematics in science and engineering |
| spelling | Jeffrey, Alan Verfasser aut Non-linear wave propagation with applications to physics and magnetohydrodynamics A. Jeffrey ; T. Taniuti 2. print. New York [u.a.] Acad. Press 1966 IX, 369 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics in science and engineering 9 Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Magnetohydrodynamik (DE-588)4130803-7 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Nichtlineare Welle (DE-588)4042102-8 s DE-604 Wellenausbreitung (DE-588)4121912-0 s Wellengleichung (DE-588)4065315-8 s Magnetohydrodynamik (DE-588)4130803-7 s Taniuti, Tosiya Verfasser aut Mathematics in science and engineering 9 (DE-604)BV000001196 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jeffrey, Alan Taniuti, Tosiya Non-linear wave propagation with applications to physics and magnetohydrodynamics Mathematics in science and engineering Nichtlineare Welle (DE-588)4042102-8 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd Wellenausbreitung (DE-588)4121912-0 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4042102-8 (DE-588)4130803-7 (DE-588)4121912-0 (DE-588)4065315-8 |
| title | Non-linear wave propagation with applications to physics and magnetohydrodynamics |
| title_auth | Non-linear wave propagation with applications to physics and magnetohydrodynamics |
| title_exact_search | Non-linear wave propagation with applications to physics and magnetohydrodynamics |
| title_full | Non-linear wave propagation with applications to physics and magnetohydrodynamics A. Jeffrey ; T. Taniuti |
| title_fullStr | Non-linear wave propagation with applications to physics and magnetohydrodynamics A. Jeffrey ; T. Taniuti |
| title_full_unstemmed | Non-linear wave propagation with applications to physics and magnetohydrodynamics A. Jeffrey ; T. Taniuti |
| title_short | Non-linear wave propagation |
| title_sort | non linear wave propagation with applications to physics and magnetohydrodynamics |
| title_sub | with applications to physics and magnetohydrodynamics |
| topic | Nichtlineare Welle (DE-588)4042102-8 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd Wellenausbreitung (DE-588)4121912-0 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Nichtlineare Welle Magnetohydrodynamik Wellenausbreitung Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001258533&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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