Blowup for nonlinear hyperbolic equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
1995
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 107 - 112 |
| Beschreibung: | XIV, 112 S. |
| ISBN: | 0817638105 3764338105 |
Internformat
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| 100 | 1 | |a Alinhac, Serge |d 1948- |e Verfasser |0 (DE-588)143378716 |4 aut | |
| 245 | 1 | 0 | |a Blowup for nonlinear hyperbolic equations |c Serge Alinhac |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1995 | |
| 300 | |a XIV, 112 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 17 | |
| 500 | |a Literaturverz. S. 107 - 112 | ||
| 650 | 7 | |a Cauchy, problème de |2 ram | |
| 650 | 7 | |a Equations différentielles hyperboliques - Solutions numériques |2 ram | |
| 650 | 4 | |a Blowing up (Algebraic geometry) | |
| 650 | 4 | |a Cauchy problem | |
| 650 | 4 | |a Differential equations, Hyperbolic |x Numerical solutions | |
| 650 | 0 | 7 | |a Nichtlineare hyperbolische Differentialgleichung |0 (DE-588)4228136-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Aufblasung |0 (DE-588)4139570-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare hyperbolische Differentialgleichung |0 (DE-588)4228136-2 |D s |
| 689 | 0 | 1 | |a Aufblasung |0 (DE-588)4139570-0 |D s |
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Datensatz im Suchindex
| _version_ | 1804124628637974528 |
|---|---|
| adam_text | CONTENTS
CHAPTER I. The Two Basic Blowup Mechanisms
Introduction 1
A. The ODE mechanism 2
1. Systems of ODE 2
2. Strictly hyperbolic semilinear systems in the plane 3
3. Semilinear wave equations 6
B. The geometric blowup mechanism 9
1. Burgers equation and the method of characteristics 9
2. Blowup of a quasilinear system 12
3. Blowup solutions 14
4. How to solve the blowup system 18
5. How Vu blows up 19
6. Singular solutions and explosive solutions 20
C. Combinations of the two mechanisms 22
1. Which mechanism takes place first? 22
2. Simultaneous occurrence of the two mechanisms 23
Notes 24
CHAPTER II. First Concepts on Global Cauchy Problems... 25
Introduction 25
1. Short time existence 26
2. Lifespan and blowup criterion 27
3. Blowup or not? Functional methods 30
a. A functional method for Burgers equation 30
b. Semilinear wave equation 32
c. The Euler system 33
4. Blowup or not? Comparison and averaging methods 36
Notes 39
vi Contents
CHAPTER III. Semilinear Wave Equations
Introduction 40
1. Semilinear blowup criteria 40
2. Maximal influence domain 42
3. Maximal influence domains for weak solutions 43
4. Blowup rates at the boundary of the maximal
influence domain 50
5. An example of a sharp estimate of the lifespan 55
Notes 57
CHAPTER IV. Quasilinear Systems in One
Space Dimension 59
Introduction 59
1. The scalar case 60
2. Riemann invariants, simple waves, and L1 boundedness 61
3. The case of 2 x 2 systems 64
4. General systems with small data 69
5. Rotationally invariant wave equations 76
Notes 80
CHAPTER V. Nonlinear Geometrical Optics
and Applications 82
Introduction 82
1. Quasilinear systems in one space dimension 83
1.1. Formal analysis 84
1.2. Slow time and reduced equations 86
1.3. Existence, approximation and blowup 89
2. Quasilinear wave equations 93
2.1. Formal analysis 93
2.2. Slow time and reduced equations 95
2.3. Existence, null conditions, blowup 97
3. Further results on the wave equation 99
Contents vii
3.1. Formal analysis near the boundary of the light cone 100
3.2. Slow time and reduced equations 101
3.3. A local blowup problem 102
3.4. Asymptotic lifespan for the two dimensional
wave equation 104
Notes 105
BIBLIOGRAPHY 107
INDEX 113
|
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| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010219361 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:41Z |
| institution | BVB |
| isbn | 0817638105 3764338105 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006791635 |
| oclc_num | 31970334 |
| open_access_boolean | |
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| owner_facet | DE-91G DE-BY-TUM DE-12 DE-29T DE-634 DE-11 DE-188 |
| physical | XIV, 112 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Alinhac, Serge 1948- Verfasser (DE-588)143378716 aut Blowup for nonlinear hyperbolic equations Serge Alinhac Boston ; Basel ; Berlin Birkhäuser 1995 XIV, 112 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 17 Literaturverz. S. 107 - 112 Cauchy, problème de ram Equations différentielles hyperboliques - Solutions numériques ram Blowing up (Algebraic geometry) Cauchy problem Differential equations, Hyperbolic Numerical solutions Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd rswk-swf Aufblasung (DE-588)4139570-0 gnd rswk-swf Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 s Aufblasung (DE-588)4139570-0 s DE-604 Progress in nonlinear differential equations and their applications 17 (DE-604)BV007934389 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006791635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alinhac, Serge 1948- Blowup for nonlinear hyperbolic equations Progress in nonlinear differential equations and their applications Cauchy, problème de ram Equations différentielles hyperboliques - Solutions numériques ram Blowing up (Algebraic geometry) Cauchy problem Differential equations, Hyperbolic Numerical solutions Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Aufblasung (DE-588)4139570-0 gnd |
| subject_GND | (DE-588)4228136-2 (DE-588)4139570-0 |
| title | Blowup for nonlinear hyperbolic equations |
| title_auth | Blowup for nonlinear hyperbolic equations |
| title_exact_search | Blowup for nonlinear hyperbolic equations |
| title_full | Blowup for nonlinear hyperbolic equations Serge Alinhac |
| title_fullStr | Blowup for nonlinear hyperbolic equations Serge Alinhac |
| title_full_unstemmed | Blowup for nonlinear hyperbolic equations Serge Alinhac |
| title_short | Blowup for nonlinear hyperbolic equations |
| title_sort | blowup for nonlinear hyperbolic equations |
| topic | Cauchy, problème de ram Equations différentielles hyperboliques - Solutions numériques ram Blowing up (Algebraic geometry) Cauchy problem Differential equations, Hyperbolic Numerical solutions Nichtlineare hyperbolische Differentialgleichung (DE-588)4228136-2 gnd Aufblasung (DE-588)4139570-0 gnd |
| topic_facet | Cauchy, problème de Equations différentielles hyperboliques - Solutions numériques Blowing up (Algebraic geometry) Cauchy problem Differential equations, Hyperbolic Numerical solutions Nichtlineare hyperbolische Differentialgleichung Aufblasung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006791635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT alinhacserge blowupfornonlinearhyperbolicequations |