Front tracking for hyperbolic conservation laws:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2015]
|
| Ausgabe: | 2nd edition |
| Schriftenreihe: | Applied mathematical sciences
152 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xiv, 515 Seiten Diagramme |
| ISBN: | 9783662475065 3662475065 |
Internformat
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| 245 | 1 | 0 | |a Front tracking for hyperbolic conservation laws |c Helge Holden, Nils Henrik Risebro |
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| 653 | |a hyperbolic partial differential equations | ||
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Datensatz im Suchindex
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CONTENTS
1 INTRODUCTION 1
1.1 LINEAR EQUATIONS 16
1.2 NOTES 45
1.3 EXERCISES 46
2 SCALAR CONSERVATION LAWS 53
2.1 ENTROPY CONDITIONS 53
2.2 THE RIEMANN PROBLEM 60
2.3 FRONT TRACKING 66
2.4 EXISTENCE AND UNIQUENESS 74
2.5 NOTES 88
2.6 EXERCISES 89
3 A SHORT COURSE IN DIFFERENCE METHODS 95
3.1 CONSERVATIVE METHODS 95
3.2 HIGHER-ORDER SCHEMES 115
3.3 ERROR ESTIMATES 127
3.4 A PRIORI ERROR ESTIMATES 139
3.5 MEASURE-VALUED SOLUTIONS 147
3.6 NOTES 165
3.7 EXERCISES 165
4 MULTIDIMENSIONAL SCALAR CONSERVATION LAWS 171
4.1 DIMENSIONAL SPLITTING METHODS 171
4.2 DIMENSIONAL SPLITTING AND FRONT TRACKING 180
4.3 CONVERGENCE RATES 189
4.4 OPERATOR SPLITTING: DIFFUSION 205
4.5 OPERATOR SPLITTING: SOURCE 212
4.6 NOTES 217
4.7 EXERCISES 217
5 THE RIEMANN PROBLEM FOR SYSTEMS 223
5.1 HYPERBOLICITY AND SOME EXAMPLES 223
5.2 RAREFACTION WAVES 229
XIII
HTTP://D-NB.INFO/1071250132
XIV CONTENTS
5.3 THE HUGONIOT LOCUS: THE SHOCK CURVES 235
5.4 THE ENTROPY CONDITION 241
5.5 THE SOLUTION OF THE RIEMANN PROBLEM 249
5.6 THE RIEMANN PROBLEM FOR THE EULER EQUATIONS 260
5.7 NOTES 277
5.8 EXERCISES 277
6 EXISTENCE OF SOLUTIONS OF THE CAUCHY PROBLEM 283
6.1 FRONT TRACKING FOR SYSTEMS 283
6.2 CONVERGENCE 297
6.3 NOTES 310
6.4 EXERCISES 311
7 WELL-POSEDNESS OF THE CAUCHY PROBLEM 313
7.1 STABILITY 318
7.2 UNIQUENESS 344
7.3 NOTES 366
7.4 EXERCISES 366
8 CONSERVATION LAWS WITH DISCONTINUOUS FLUX FUNCTIONS 367
8.1 THE RIEMANN PROBLEM 369
8.2 THE CAUCHY PROBLEM 391
8.3 UNIQUENESS OF ENTROPY SOLUTIONS 412
8.4 NOTES 425
8.5 EXERCISES 426
A TOTAL VARIATION, COMPACTNESS, ETC 427
A.L NOTES 438
A.2 EXERCISES 439
B THE METHOD OF VANISHING VISCOSITY 441
B.L NOTES 455
B.2 EXERCISES 456
C ANSWERS AND HINTS 457
BIBLIOGRAPHY 503
INDEX 513 |
| any_adam_object | 1 |
| author | Holden, Helge 1956- Risebro, Nils Henrik |
| author_GND | (DE-588)111693667 |
| author_facet | Holden, Helge 1956- Risebro, Nils Henrik |
| author_role | aut aut |
| author_sort | Holden, Helge 1956- |
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| building | Verbundindex |
| bvnumber | BV043303707 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)910328663 (DE-599)DNB1071250132 |
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| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515/.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd edition |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-09-10T01:58:24Z |
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| language | English |
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| physical | xiv, 515 Seiten Diagramme |
| publishDate | 2015 |
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| publisher | Springer |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Holden, Helge 1956- Verfasser (DE-588)111693667 aut Front tracking for hyperbolic conservation laws Helge Holden, Nils Henrik Risebro 2nd edition Berlin ; Heidelberg Springer [2015] © 2015 xiv, 515 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 152 Conservation laws (Mathematics) Differential equations, Hyperbolic Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Graduate hyperbolic partial differential equations conservation laws front tracking Erhaltungssatz (DE-588)4131214-4 s Hyperbolisches System (DE-588)4191897-6 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Risebro, Nils Henrik Verfasser aut Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 10.1007/978-3-662-47507-2 Erscheint auch als Online-Ausgabe 978-3-662-47507-2 Applied mathematical sciences 152 (DE-604)BV000005274 152 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5266827&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028724516&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holden, Helge 1956- Risebro, Nils Henrik Front tracking for hyperbolic conservation laws Applied mathematical sciences Conservation laws (Mathematics) Differential equations, Hyperbolic Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4131214-4 (DE-588)4191897-6 (DE-588)4128130-5 |
| title | Front tracking for hyperbolic conservation laws |
| title_auth | Front tracking for hyperbolic conservation laws |
| title_exact_search | Front tracking for hyperbolic conservation laws |
| title_full | Front tracking for hyperbolic conservation laws Helge Holden, Nils Henrik Risebro |
| title_fullStr | Front tracking for hyperbolic conservation laws Helge Holden, Nils Henrik Risebro |
| title_full_unstemmed | Front tracking for hyperbolic conservation laws Helge Holden, Nils Henrik Risebro |
| title_short | Front tracking for hyperbolic conservation laws |
| title_sort | front tracking for hyperbolic conservation laws |
| topic | Conservation laws (Mathematics) Differential equations, Hyperbolic Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Conservation laws (Mathematics) Differential equations, Hyperbolic Erhaltungssatz Hyperbolisches System Numerisches Verfahren |
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