Hyperbolic systems of conservation laws: the theory of classical and nonclassical shock waves
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
2002
|
| Series: | Lectures in mathematics : ETH Zürich
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 271 - 204 |
| Physical Description: | X, 294 S. graph. Darst. |
| ISBN: | 3764366877 |
Staff View
MARC
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| 245 | 1 | 0 | |a Hyperbolic systems of conservation laws |b the theory of classical and nonclassical shock waves |c Philippe G. LeFloch |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 2002 | |
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| 490 | 0 | |a Lectures in mathematics : ETH Zürich | |
| 500 | |a Literaturverz. S. 271 - 204 | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
Chapter I. Fundamental concepts and examples
1.
Hyperbolicity, genuine nonlinearity, and entropies
1
2.
Shock formation and weak solutions
8
3.
Singular limits and the entropy inequality
13
4.
Examples of diffusive-dispersive models
17
5.
Kinetic relations and traveling waves
22
Part
1.
SCALAR CONSERVATION LAWS
Chapter II. The Riemann problem
1.
Entropy conditions
29
2.
Classical Riemann solver
31
3.
Entropy dissipation function
36
4.
Nonclassical Riemann solver for concave-convex flux
41
5.
Nonclassical Riemann solver for convex-concave flux
47
Chapter III. Diffusive-dispersive traveling waves
1.
Diffusive traveling waves
51
2.
Kinetic functions for the cubic flux
53
3.
Kinetic functions for general flux
59
4.
Traveling waves for a given speed
68
5.
Traveling waves for a given diffusion-dispersion ratio
77
Chapter IV. Existence theory for the Cauchy problem
1.
Classical entropy solutions for convex flux
81
2.
Classical entropy solutions for general flux
88
3.
Nonclassical entropy solutions
93
4.
Refined estimates
112
Chapter V. Continuous dependence of solutions
1.
A class of linear hyperbolic equations
118
2.
L1 continuous dependence estimate
126
3.
Sharp version of the continuous dependence estimate
133
4.
Generalizations
135
viii CONTENTS
Part
2.
SYSTEMS OF CONSERVATION LAWS
Chapter VI. The Riemann problem
1.
Shock and rarefaction waves
139
2.
Classical Riemann solver
148
3.
Entropy dissipation and wave sets
156
4.
Kinetic relation and nonclassical Riemann solver
163
Chapter
VII.
Classical entropy solutions of the Cauchy problem
1. Glimm
interaction estimates
167
2.
Existence theory
176
3.
Uniform estimates
180
4.
Pointwise regularity properties
186
Chapter
VIII.
Nonclassical entropy solutions of the Cauchy problem
1.
A generalized total variation functional
188
2.
A generalized weighted interaction potential
200
3.
Existence theory
206
4.
Pointwise regularity properties
211
Chapter IX. Continuous dependence of solutions
1.
A class of linear hyperbolic systems
212
2.
L1 continuous dependence estimate
223
3.
Sharp version of the continuous dependence estimate
231
4.
Generalizations
240
Chapter X. Uniqueness of entropy solutions
1.
Admissible entropy solutions
241
2.
Tangency property
246
3.
Uniqueness theory
252
4.
Applications
255
Appendix. Functions with bounded variation
259
Bibliographical notes
265
References
271
|
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| dewey-search | 515/.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014444469 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:52Z |
| institution | BVB |
| isbn | 3764366877 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009873751 |
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| physical | X, 294 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
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| series2 | Lectures in mathematics : ETH Zürich |
| spelling | LeFloch, Philippe G. Verfasser (DE-588)1154537285 aut Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves Philippe G. LeFloch Basel ; Boston ; Berlin Birkhäuser 2002 X, 294 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics : ETH Zürich Literaturverz. S. 271 - 204 Cauchy, Problème de ram Lois de conservation (mathématiques) ram Ondes de choc ram Conservation laws (Mathematics) Differential equations, Hyperbolic Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 s Nichtlineares hyperbolisches System (DE-588)4191896-4 s DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | LeFloch, Philippe G. Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves Cauchy, Problème de ram Lois de conservation (mathématiques) ram Ondes de choc ram Conservation laws (Mathematics) Differential equations, Hyperbolic Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4191896-4 (DE-588)4131214-4 (DE-588)4131213-2 |
| title | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves |
| title_auth | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves |
| title_exact_search | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves |
| title_full | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves Philippe G. LeFloch |
| title_fullStr | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves Philippe G. LeFloch |
| title_full_unstemmed | Hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves Philippe G. LeFloch |
| title_short | Hyperbolic systems of conservation laws |
| title_sort | hyperbolic systems of conservation laws the theory of classical and nonclassical shock waves |
| title_sub | the theory of classical and nonclassical shock waves |
| topic | Cauchy, Problème de ram Lois de conservation (mathématiques) ram Ondes de choc ram Conservation laws (Mathematics) Differential equations, Hyperbolic Nichtlineares hyperbolisches System (DE-588)4191896-4 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Cauchy, Problème de Lois de conservation (mathématiques) Ondes de choc Conservation laws (Mathematics) Differential equations, Hyperbolic Nichtlineares hyperbolisches System Erhaltungssatz Hyperbolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873751&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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