Systems of conservation laws: 1 Hyperbolicity, entropies, shock waves
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1999
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| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008691686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 263 S. |
| ISBN: | 0521582334 |
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| 245 | 1 | 0 | |a Systems of conservation laws |n 1 |p Hyperbolicity, entropies, shock waves |c Denis Serre |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Acknowledgments page xi
Introduction xiii
1 Some models 1
1.1 Gas dynamics in eulerian variables 1
1.2 Gas dynamics in lagrangian variables 8
1.3 The equation of road traffic 10
1.4 Electromagnetism 11
1.5 Magneto hydrodynamics 14
1.6 Hyperelastic materials 17
1.7 Singular limits of dispersive equations 19
1.8 Electrophoresis 22
2 Scalar equations in dimension d = 1 25
2.1 Classical solutions of the Cauchy problem 25
2.2 Weak solutions, non uniqueness 27
2.3 Entropy solutions, the Kruzkov existence theorem 32
2.4 The Riemann problem 43
2.5 The case of / convex. The Lax formula 45
2.6 Proof of Theorem 2.3.5: existence 47
2.7 Proof of Theorem 2.3.5: uniqueness 51
2.8 Comments 57
2.9 Exercises 60
3 Linear and quasi linear systems 68
3.1 Linear hyperbolic systems 69
3.2 Quasi linear hyperbolic systems 79
vii
viii Contents
3.3 Conservative systems 80
3.4 Entropies, convexity and hyperbolicity 82
3.5 Weak solutions and entropy solutions 86
3.6 Local existence of smooth solutions 91
3.7 The wave equation 101
4 Dimension d = 1, the Riemann problem 106
4.1 Generalities on the Riemann problem 106
4.2 The Hugoniot locus 107
4.3 Shockwaves 111
4.4 Contact discontinuities 116
4.5 Rarefaction waves. Wave curves 119
4.6 Lax s theorem 122
4.7 The solution of the Riemann problem for the /7 system 127
4.8 The solution of the Riemann problem for gas dynamics 132
4.9 Exercises 143
5 The Glimm scheme 146
5.1 Functions of bounded variation 146
5.2 Description of the scheme 149
5.3 Consistency 153
5.4 Convergence 156
5.5 Stability 161
5.6 The example of Nishida 167
5.7 2x2 Systems with diminishing total variation 174
5.8 Technical lemmas 177
5.9 Supplementary remarks 180
5.10 Exercises 182
6 Second order perturbations 186
6.1 Dissipation by viscosity 187
6.2 Global existence in the strictly dissipative case 193
6.3 Smooth convergence as s 0+ 203
6.4 Scalar case. Accuracy of approximation 210
6.5 Exercises 216
7 Viscosity profiles for shock waves 220
7.1 Typical example of a limit of viscosity solutions 220
7.2 Existence of the viscosity profile for a weak shock 225
7.3 Profiles for gas dynamics 229
Contents ix
7.4 Asymptotic stability 230
7.5 Stability of the profile for a Lax shock 235
7.6 Influence of the diffusion tensor 242
7.7 Case of over compressive shocks 245
7.8 Exercises 250
Bibliography 255
Index 261
|
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| id | DE-604.BV012779990 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:36:07Z |
| institution | BVB |
| isbn | 0521582334 |
| language | English |
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| oclc_num | 60141187 |
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| physical | XXII, 263 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Serre, Denis 1954- Systems of conservation laws Conservation laws (Mathematics) |
| title | Systems of conservation laws |
| title_alt | Systèmes de lois de conservation |
| title_auth | Systems of conservation laws |
| title_exact_search | Systems of conservation laws |
| title_full | Systems of conservation laws 1 Hyperbolicity, entropies, shock waves Denis Serre |
| title_fullStr | Systems of conservation laws 1 Hyperbolicity, entropies, shock waves Denis Serre |
| title_full_unstemmed | Systems of conservation laws 1 Hyperbolicity, entropies, shock waves Denis Serre |
| title_short | Systems of conservation laws |
| title_sort | systems of conservation laws hyperbolicity entropies shock waves |
| topic | Conservation laws (Mathematics) |
| topic_facet | Conservation laws (Mathematics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008691686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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