Hyperbolic partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 150 S. 235 mm x 155 mm |
| ISBN: | 9780387878225 |
Staff View
MARC
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| 100 | 1 | |a Alinhac, Serge |d 1948- |e Verfasser |0 (DE-588)143378716 |4 aut | |
| 245 | 1 | 0 | |a Hyperbolic partial differential equations |c Serge Alinhac |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XI, 150 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 7 | |a Équations différentielles hyperboliques |2 ram | |
| 650 | 4 | |a Differential equations, Hyperbolic | |
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| 689 | 0 | 0 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |D s |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-87823-2 |
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Record in the Search Index
| _version_ | 1804139225801555968 |
|---|---|
| adam_text | Contents
Introduction
ix
1
Vector
Fields and Integral Curves
1
1.1
First Definitions
........................ 1
1.2
Flows
.............................. 2
1.3
Directional Derivatives
..................... 3
1.4
Level Surfaces
.......................... 4
1.5
Bracket of Two Fields
..................... 5
1.6
Cauchy Problem and Method of Characteristics
....... 5
1.7
Stopping Time
......................... 8
1.8
Straightening Out of a Field
.................. 8
1.9
Propagation of Regularity
................... 9
1.10
Exercises
............................ 9
2
Operators and Systems in the Plane
13
2.1
Operators in the Plane: First Definitions
........... 13
2.2
Systems in the Plane: First Definitions
............ 15
2.3
Reducing an Operator to a System
.............. 16
2.4
Gronwall Lemma
........................ 18
2.5
Domains of Determination I (A priori Estimate)
...... 19
■yj Contents
2.6
Domains of Determination II (Existence)
.......... 21
2.7
Exercises
............................ 22
3
Nonlinear First Order Equations
27
3.1
Quasilinear Scalar Equations
................. 27
3.2
Eikonal Equations
....................... 30
3.3
Exercises
............................ 35
3.4
Notes
.............................. 40
4
Conservation Laws in One-Space Dimension
41
4.1
First Definitions and Examples
................ 41
4.2
Examples of Singular Solutions
................ 42
4.3
Simple Waves
.......................... 44
4.4
Rarefaction Waves
....................... 46
4.5
Riemann Invariants
....................... 47
4.6
Shock Curves
.......................... 48
4.7
Lax Conditions and Admissible Shocks
............ 50
4.8
Contact Discontinuities
.................... 52
4.9
Riemann Problem
....................... 53
4.10
Viscosity and Entropy
..................... 54
4.10.1
Entropy
......................... 55
4.10.2
Limits of Viscosity Solutions
............. 55
4.10.3
Application to the Case of a Shock
.......... 56
4.11
Exercises
............................ 58
4.12
Notes
.................... 52
5
The Wave Equation g5
5.1
Explicit Solutions
............... 55
5.1.1
Fourier Analysis
............ 66
Contents
vii
5.1.2 Solutions
as Spherical Means
............. 67
5.1.3
Finite Speed of Propagation, Domains of
Determination
..................... 68
5.1.4
Strong Huygens Principle
............... 69
5.1.5
Asymptotic Behavior of Solutions
........... 69
5.2
Geometry of The Wave Equation
............... 70
5.2.1
Rotations and Scaling Vector Field
.......... 71
5.2.2
Hyperbolic Rotations and
Lorentz
Fields
...... 74
5.2.3
Light Cones, Null Frames, and Good Derivatives
. . 75
5.2.4
Klainerman s Inequality
................ 77
5.3
Exercises
............................ 79
5.4
Notes
.............................. 82
6
Energy Inequalities for the Wave Equation
83
6.1
Standard Inequality in a Strip
................ 83
6.2
Improved Standard Inequality
................. 86
6.3
Inequalities in a Domain
.................... 88
6.4
General Multipliers
....................... 90
6.5
Morawetz Inequality
...................... 92
6.6
KSS
Inequality
......................... 94
6.7
Conformai
Inequality
...................... 98
6.8
Exercises
............................ 102
6.9
Notes
.............................. 110
7
Variable Coefficient Wave Equations and Systems 111
7.1
What is a Wave Equation?
..................
Ill
7.2
Energy Inequality for the Wave Equation
.......... 112
7.3
Symmetric Systems
...................... 115
7.3.1
Definitions and Examples
............... 115
viii Contents
7.3.2
Energy
Inequality
................... 117
7.4
Finite
Speed of Propagation
.................. 118
7.5
Klainerman s Method
..................... 120
7.6
Existence of Smooth Solutions
................ 123
7.7
Geometrical Optics
....................... 126
7.7.1
An Algebraic Computation
.............. 126
7.7.2
Formal and Actual Geometrical Optics
........ 127
7.7.3
Parametrics for the Cauchy Problem
......... 128
7.8
Exercises
............................ 130
7.9
Notes
.............................. 135
Appendix
137
A.I Ordinary Differential Equations
................ 137
АЛЛ
Cauchy Problem
.................... 137
A.1.2 Flows
.......................... 140
A.1.3 Lower and Upper Fences
................ 141
A.2 Submanifolds
.......................... 141
A.2.1 First Definitions
.................... 141
A.2.
2
Submanifolds Defined by Equations
......... 142
A.2.3 Parametrized Surfaces
................. 143
A.2.4 Graphs
......................... 144
A.2.5 Weaving
......................... 145
A.2.6 Stokes Formula
..................... 145
References
147
Index
149
|
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| dewey-sort | 3515 43535 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035571872 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:40:42Z |
| institution | BVB |
| isbn | 9780387878225 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017627442 |
| oclc_num | 495198418 |
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| owner_facet | DE-20 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 DE-824 DE-188 DE-29T |
| physical | XI, 150 S. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Alinhac, Serge 1948- Verfasser (DE-588)143378716 aut Hyperbolic partial differential equations Serge Alinhac New York, NY Springer 2009 XI, 150 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Universitext Équations différentielles hyperboliques ram Differential equations, Hyperbolic Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-87823-2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017627442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alinhac, Serge 1948- Hyperbolic partial differential equations Équations différentielles hyperboliques ram Differential equations, Hyperbolic Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4131213-2 |
| title | Hyperbolic partial differential equations |
| title_auth | Hyperbolic partial differential equations |
| title_exact_search | Hyperbolic partial differential equations |
| title_full | Hyperbolic partial differential equations Serge Alinhac |
| title_fullStr | Hyperbolic partial differential equations Serge Alinhac |
| title_full_unstemmed | Hyperbolic partial differential equations Serge Alinhac |
| title_short | Hyperbolic partial differential equations |
| title_sort | hyperbolic partial differential equations |
| topic | Équations différentielles hyperboliques ram Differential equations, Hyperbolic Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Équations différentielles hyperboliques Differential equations, Hyperbolic Hyperbolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017627442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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