Lectures on non-linear wave equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Internat. Press
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 204 S. |
| ISBN: | 9781571461735 1571461736 |
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MARC
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| 245 | 1 | 0 | |a Lectures on non-linear wave equations |c Christopher D. Sogge |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Internat. Press |c 2008 | |
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Record in the Search Index
| _version_ | 1804137947890450432 |
|---|---|
| adam_text | CONTENTS
Preface
to the Second Edition
Preface
Chapter I. Background and groundwork
§1.
Linear wave equation: a review
1
§2.
Energy inequality: a first version
12
§3.
Existence and uniqueness for linear equations
18
§4.
Local existence for
quasilinear
equations
25
§5.
Local existence for
semilinear
equations in
(1 +
3)-dimensions
32
Notes
38
Chapter II. Quasilinear equations with small data
§1.
Klainerman-Sobolev inequalities
39
§2.
Global existence in higher dimensions
50
§3.
A weighted energy estimate
58
§4.
Almost global existence for symmetric systems
62
§5.
Null condition and global existence when
η
= 3 71
§6.
The restriction theorem and local existence revis¬
ited
84
Notes
93
Chapter III. Semilinear equations with small data
§1.
Strichartz s estimate for the wave equation
95
§2.
John s existence theorem for
Ж1+3
108
§3.
Blow-up for small powers
114
Notes
120
Chapter IV. General Strichartz estimates
§1.
The endpoint Strichartz estimates of Keel and Tao
121
§2.
The Christ-Kiselev lemma and inhomogeneous es¬
timates
136
§3.
An application: Existence theorems for rough data
141
§4.
Improved results under spherical symmetry
154
Notes
162
CONTENTS
Chapter V.
Global existence
for semilinear equa¬
tions with large data
§1.
Main results
165
§2.
Energy estimates and the subcritical case
171
§3.
A decay lemma and the critical case
174
Notes
185
Appendix: Some tools from classical analysis
186
Bibliography
196
Index
204
Index of notation
204
|
| adam_txt |
CONTENTS
Preface
to the Second Edition
Preface
Chapter I. Background and groundwork
§1.
Linear wave equation: a review
1
§2.
Energy inequality: a first version
12
§3.
Existence and uniqueness for linear equations
18
§4.
Local existence for
quasilinear
equations
25
§5.
Local existence for
semilinear
equations in
(1 +
3)-dimensions
32
Notes
38
Chapter II. Quasilinear equations with small data
§1.
Klainerman-Sobolev inequalities
39
§2.
Global existence in higher dimensions
50
§3.
A weighted energy estimate
58
§4.
Almost global existence for symmetric systems
62
§5.
Null condition and global existence when
η
= 3 71
§6.
The restriction theorem and local existence revis¬
ited
84
Notes
93
Chapter III. Semilinear equations with small data
§1.
Strichartz's estimate for the wave equation
95
§2.
John's existence theorem for
Ж1+3
108
§3.
Blow-up for small powers
114
Notes
120
Chapter IV. General Strichartz estimates
§1.
The endpoint Strichartz estimates of Keel and Tao
121
§2.
The Christ-Kiselev lemma and inhomogeneous es¬
timates
136
§3.
An application: Existence theorems for rough data
141
§4.
Improved results under spherical symmetry
154
Notes
162
CONTENTS
Chapter V.
Global existence
for semilinear equa¬
tions with large data
§1.
Main results
165
§2.
Energy estimates and the subcritical case
171
§3.
A decay lemma and the critical case
174
Notes
185
Appendix: Some tools from classical analysis
186
Bibliography
196
Index
204
Index of notation
204 |
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| author | Sogge, Christopher D. 1960- |
| author_GND | (DE-588)104999275X |
| author_facet | Sogge, Christopher D. 1960- |
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| author_sort | Sogge, Christopher D. 1960- |
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| ctrlnum | (OCoLC)493910071 (DE-599)BVBBV035021533 |
| dewey-full | 531.113 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.113 |
| dewey-search | 531.113 |
| dewey-sort | 3531.113 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:46:35Z |
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| institution | BVB |
| isbn | 9781571461735 1571461736 |
| language | English |
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| physical | 204 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Internat. Press |
| record_format | marc |
| spelling | Sogge, Christopher D. 1960- Verfasser (DE-588)104999275X aut Lectures on non-linear wave equations Christopher D. Sogge 2. ed. Boston [u.a.] Internat. Press 2008 204 S. txt rdacontent n rdamedia nc rdacarrier Équations d'onde non linéaires ram Nonlinear wave equations Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016690641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sogge, Christopher D. 1960- Lectures on non-linear wave equations Équations d'onde non linéaires ram Nonlinear wave equations Nichtlineare Wellengleichung (DE-588)4042104-1 gnd |
| subject_GND | (DE-588)4042104-1 |
| title | Lectures on non-linear wave equations |
| title_auth | Lectures on non-linear wave equations |
| title_exact_search | Lectures on non-linear wave equations |
| title_exact_search_txtP | Lectures on non-linear wave equations |
| title_full | Lectures on non-linear wave equations Christopher D. Sogge |
| title_fullStr | Lectures on non-linear wave equations Christopher D. Sogge |
| title_full_unstemmed | Lectures on non-linear wave equations Christopher D. Sogge |
| title_short | Lectures on non-linear wave equations |
| title_sort | lectures on non linear wave equations |
| topic | Équations d'onde non linéaires ram Nonlinear wave equations Nichtlineare Wellengleichung (DE-588)4042104-1 gnd |
| topic_facet | Équations d'onde non linéaires Nonlinear wave equations Nichtlineare Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016690641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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