Front tracking for hyperbolic conservation laws:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2007
|
| Ausgabe: | 2., corr. print. |
| Schriftenreihe: | Applied mathematical sciences
152 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XI, 363 S. graph. Darst. |
| ISBN: | 3540432892 9783540432890 |
Internformat
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| 245 | 1 | 0 | |a Front tracking for hyperbolic conservation laws |c Helge Holden ; Nils Henrik Risebro |
| 250 | |a 2., corr. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2007 | |
| 300 | |a XI, 363 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 152 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 0 | 7 | |a Hyperbolisches System |0 (DE-588)4191897-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Erhaltungssatz |0 (DE-588)4131214-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Erhaltungssatz |0 (DE-588)4131214-4 |D s |
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| 689 | 0 | 2 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Risebro, Nils Henrik |e Sonstige |4 oth | |
| 830 | 0 | |a Applied mathematical sciences |v 152 |w (DE-604)BV000005274 |9 152 | |
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Datensatz im Suchindex
| _version_ | 1804137375756976128 |
|---|---|
| adam_text | Contents
Preface
vii
1
Introduction
1
1.1
Notes
............................. 18
2
Scalar
Conservation
Laws
23
2.1
Entropy Conditions
..................... 24
2.2
The Riemann Problem
................... 30
2.3
Front Tracking
........................ 36
2.4
Existence and Uniqueness
................. 44
2.5
Notes
............................. 56
3
A Short Course in Difference Methods
63
3.1
Conservative Methods
................... 63
3.2
Error Estimates
....................... 81
3.3
A Priori Error Estimates
.................. 92
3.4
Measure-Valued Solutions
................. 99
3.5
Notes
............................. 112
4
Multidimensional Scalar Conservation Laws
117
4.1
Dimensional Splitting Methods
.............. 117
4.2
Dimensional Splitting and Front Tracking
........ 126
4.3
Convergence Rates
..................... 134
4.4
Operator Splitting: Diffusion
................ 146
xii Contents
4.5 Operator Splitting:
Source
................. 153
4.6 Notes............................. 157
5 The Riemann Problem
for
Systems 163
5.1
Hvperbolicity and Some Examples.............
164
5.2
Rarefaction Waves
...................... 168
5.3
The Hugoniot Locus: The Shock Curves
......... 174
5.4
The Entropy Condition
................... 180
5.5
The Solution of the Riemann Problem
.......... 188
5.6
Notes
............................. 200
6
Existence of Solutions of the Cauchy Problem
205
6.1
Front Tracking for Systems
................. 206
6.2
Convergence
......................... 218
6.3
Notes
............................. 229
7
Well-Posedness of the Cauchy Problem
233
7.1
Stability
........................... 238
7.2
Uniqueness
.......................... 265
7.3
Notos
............................. 285
A Total Variation, Compactness, etc.
287
A.I Notes
............................. 298
8
The Method of Vanishing Viscosity
299
B.I Notes
............................. 312
С
Answers and Hints
315
References
349
Index
359
|
| adam_txt |
Contents
Preface
vii
1
Introduction
1
1.1
Notes
. 18
2
Scalar
Conservation
Laws
23
2.1
Entropy Conditions
. 24
2.2
The Riemann Problem
. 30
2.3
Front Tracking
. 36
2.4
Existence and Uniqueness
. 44
2.5
Notes
. 56
3
A Short Course in Difference Methods
63
3.1
Conservative Methods
. 63
3.2
Error Estimates
. 81
3.3
A Priori Error Estimates
. 92
3.4
Measure-Valued Solutions
. 99
3.5
Notes
. 112
4
Multidimensional Scalar Conservation Laws
117
4.1
Dimensional Splitting Methods
. 117
4.2
Dimensional Splitting and Front Tracking
. 126
4.3
Convergence Rates
. 134
4.4
Operator Splitting: Diffusion
. 146
xii Contents
4.5 Operator Splitting:
Source
. 153
4.6 Notes. 157
5 The Riemann Problem
for
Systems 163
5.1
Hvperbolicity and Some Examples.
164
5.2
Rarefaction Waves
. 168
5.3
The Hugoniot Locus: The Shock Curves
. 174
5.4
The Entropy Condition
. 180
5.5
The Solution of the Riemann Problem
. 188
5.6
Notes
. 200
6
Existence of Solutions of the Cauchy Problem
205
6.1
Front Tracking for Systems
. 206
6.2
Convergence
. 218
6.3
Notes
. 229
7
Well-Posedness of the Cauchy Problem
233
7.1
Stability
. 238
7.2
Uniqueness
. 265
7.3
Notos
. 285
A Total Variation, Compactness, etc.
287
A.I Notes
. 298
8
The Method of Vanishing Viscosity
299
B.I Notes
. 312
С
Answers and Hints
315
References
349
Index
359 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2., corr. print. |
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| id | DE-604.BV023112158 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:48:39Z |
| indexdate | 2024-07-09T21:11:18Z |
| institution | BVB |
| isbn | 3540432892 9783540432890 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016314734 |
| oclc_num | 587701443 |
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| owner | DE-355 DE-BY-UBR DE-706 |
| owner_facet | DE-355 DE-BY-UBR DE-706 |
| physical | XI, 363 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| 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 2., corr. print. New York [u.a.] Springer 2007 XI, 363 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 152 Hier auch später erschienene, unveränderte Nachdrucke Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf 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 Sonstige oth Applied mathematical sciences 152 (DE-604)BV000005274 152 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016314734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holden, Helge 1956- Front tracking for hyperbolic conservation laws Applied mathematical sciences Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolisches System (DE-588)4191897-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4191897-6 (DE-588)4131214-4 |
| 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_exact_search_txtP | 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 | Numerisches Verfahren (DE-588)4128130-5 gnd Hyperbolisches System (DE-588)4191897-6 gnd Erhaltungssatz (DE-588)4131214-4 gnd |
| topic_facet | Numerisches Verfahren Hyperbolisches System Erhaltungssatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016314734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT holdenhelge fronttrackingforhyperbolicconservationlaws AT risebronilshenrik fronttrackingforhyperbolicconservationlaws |