Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
EMS Press
[2022]
|
| Schriftenreihe: | Memoirs of the European Mathematical Society
Vol. 1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 280 Seiten Illustrationen 24 cm x 17 cm |
| ISBN: | 9783985470204 3985470200 9783985475209 |
Internformat
MARC
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| 100 | 1 | |a Delort, Jean-Marc |d 1961- |0 (DE-588)1027794106 |4 aut | |
| 245 | 1 | 0 | |a Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |c Jean-Marc Delort ; Nader Masmoudi |
| 264 | 1 | |a Berlin |b EMS Press |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a ix, 280 Seiten |b Illustrationen |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the European Mathematical Society |v Vol. 1 | |
| 650 | 0 | 7 | |a Störungstheorie |0 (DE-588)4128420-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Knicksoliton |0 (DE-588)4245710-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Normalform |0 (DE-588)4172025-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wellengleichung |0 (DE-588)4065315-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dimension 1 |0 (DE-588)4323094-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Klein-Gordon-Gleichung |0 (DE-588)4164132-2 |2 gnd |9 rswk-swf |
| 653 | |a kink | ||
| 653 | |a nonlinear Klein–Gordon equations | ||
| 653 | |a normal forms | ||
| 653 | |a Fermi’s golden rule | ||
| 689 | 0 | 0 | |a Wellengleichung |0 (DE-588)4065315-8 |D s |
| 689 | 0 | 1 | |a Dimension 1 |0 (DE-588)4323094-5 |D s |
| 689 | 0 | 2 | |a Knicksoliton |0 (DE-588)4245710-5 |D s |
| 689 | 0 | 3 | |a Klein-Gordon-Gleichung |0 (DE-588)4164132-2 |D s |
| 689 | 0 | 4 | |a Störungstheorie |0 (DE-588)4128420-3 |D s |
| 689 | 0 | 5 | |a Normalform |0 (DE-588)4172025-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Masmoudi, Nader |d 1974- |0 (DE-588)1202473091 |4 aut | |
| 710 | 2 | |a European Mathematical Society Publishing House ETH-Zentrum SEW A27 |0 (DE-588)1066118477 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-98547-520-9 |
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Datensatz im Suchindex
| _version_ | 1804184641000701952 |
|---|---|
| adam_text | CONTENTS
1
INTRODUCTION
.......................................................................................................
1
1.1
LONG
TIME
EXISTENCE
FOR
PERTURBED
EVOLUTION
EQUATIONS
.........................
1
1.2
THE
USE
OF
DISPERSION
...............................................................................
2
1.3
VECTOR
FIELDS
METHODS
AND
GLOBAL
SOLUTIONS
.............................................
3
1.4
KLAINERMAN-SOBOLEV
ESTIMATES
IN
ONE
DIMENSION
.................................
6
1.5
THE
CASE
OF
LONG
RANGE
NONLINEARITIES
.......................................................
9
1.6
MORE
GENERAL
NONLINEARITIES
AND
NORMAL
FORMS
......................................
15
1.7
PERTURBATIONS
OF
NON-ZERO
STATIONARY
SOLUTION
........................................
21
1.8
THE
KINK
PROBLEM.
I
.................................................................................
24
1.9
THE
KINK
PROBLEM
II.
COUPLING
WITH
THE
BOUND
STATE
..............................
27
2
THE
KINK
PROBLEM
.............................................................................................
31
2.1
STATEMENT
OF
THE
MAIN
RESULT
.....................................................................
31
2.2
REDUCED
SYSTEM
.........................................................................................
33
2.3
STEP
1:
WRITING
OF
THE
SYSTEM
FROM
MULTILINEAR
OPERATORS
.....................
37
2.4
STEP
2:
FIRST
QUADRATIC
NORMAL
FORM
.........................................................
37
2.5
STEP
3:
APPROXIMATE
SOLUTION
...................................................................
38
2.6
STEP
4:
REDUCED
FORM
OF
DISPERSIVE
EQUATION
........................................
41
2.7
STEP
5:
NORMAL
FORMS
...............................................................................
43
2.8
STEP
6:
BOOTSTRAP
OF
L
2
ESTIMATES
...........................................................
46
2.9
STEP
7:
BOOTSTRAP
OF
L
ESTIMATES
AND
END
OF
PROOF
..............................
46
2.10
FURTHER
COMMENTS
....................................................................................
47
3
FIRST
QUADRATIC
NORMAL
FORM
..........................................................................
53
3.1
EXPRESSION
OF
THE
EQUATION
FROM
MULTILINEAR
OPERATORS
.........................
53
3.2
FIRST
QUADRATIC
NORMAL
FORM
....................................................................
56
4
CONSTRUCTION
OF
APPROXIMATE
SOLUTIONS
.........................................................
59
4.1
APPROXIMATE
SOLUTION
TO
THE
DISPERSIVE
EQUATION
...................................
59
4.2
ASYMPTOTIC
ANALYSIS
OF
THE
ODE
..............................................................
73
5
REDUCED
FORM
OF
DISPERSIVE
EQUATION
...........................................................
81
5.1
A
FIXED
POINT
THEOREM
...............................................................................
81
5.2
REDUCTION
OF
THE
DISPERSIVE
EQUATION
......................................................
87
6
NORMAL
FORMS
.......................................................................................................
103
6.1
EXPRESSION
OF
THE
EQUATION
AS
A
SYSTEM
....................................................
104
6.2
NORMAL
FORMS
.............................................................................................
108
VIII
CONTENTS
7
BOOTSTRAP:
2
ESTIMATES
..................................................................................
117
7.1
ESTIMATES
FOR
CUBIC
AND
QUARTIC
TERMS
.....................................................
117
7.2
ESTIMATES
FOR
QUADRATIC
TERMS
.....................................................................
122
7.3
HIGHER-ORDER
TERMS
......................................................................................
124
8
L
ESTIMATES
AND
END
OF
BOOTSTRAP
...............................................................
139
8.1
L
ESTIMATES
..............................................................................................
139
8.2
BOOTSTRAP
OF
L
ESTIMATES
........................................................................
145
8.3
END
OF
BOOTSTRAP
ARGUMENT
........................................................................
152
A
SCATTERING
FOR
TIME
INDEPENDENT
POTENTIAL
.....................................................
155
A.1
STATEMENT
OF
MAIN
PROPOSITION
.................................................................
155
A.2
PROOF
OF
MAIN
PROPOSITION
........................................................................
157
B
(SEMICLASSICAL)
PSEUDO-DIFFERENTIAL
OPERATORS
.............................................
165
B.1
CLASSES
OF
SYMBOLS
AND
THEIR
QUANTIZATION
.............................................
166
B.2
SYMBOLIC
CALCULUS
......................................................................................
169
C
BOUNDS
FOR
FORCED
LINEAR
KLEIN-GORDON
EQUATIONS
......................................
177
C.1
LINEAR
SOLUTIONS
TO
HALF-KLEIN-GORDON
EQUATIONS
....................................
177
C.2
ACTION
OF
LINEAR
AND
BILINEAR
OPERATORS
.....................................................
191
C.3
AN
EXPLICIT
COMPUTATION
...........................................................................
199
D
ACTION
OF
MULTILINEAR
OPERATORS
ON
SOBOLEV
AND
HOLDER
SPACES
.............
203
D.
1
ACTION
OF
QUANTIZATION
OF
NON-SPACE-DECAYING
SYMBOLS
.......................
204
D.2
ACTION
OF
QUANTIZATION
OF
SPACE
DECAYING
SYMBOLS
.................................
213
D.3
WEYL
CALCULUS
...........................................................................................
223
E
WAVE
OPERATORS
FOR
TIME
DEPENDENT
POTENTIALS
.............................................
229
E.
1
STATEMENT
OF
THE
RESULT
...............................................................................
229
E.2
TECHNICAL
LEMMAS
......................................................................................
234
E.3
PROOF
OF
PROPOSITION
E.
1.3
........................................................................
247
F
DIVISION
LEMMAS
AND
NORMAL
FORMS
..............................................................
253
F.1
DIVISION
LEMMAS
......................................................................................
253
F.2
COMMUTATION
RESULTS
.................................................................................
255
F.3
NORMAL
FORMS
FOR
NON-CHARACTERISTIC
TERMS
.............................................
258
F.4
QUADRATIC
NORMAL
FORMS
FOR
SPACE
DECAYING
SYMBOLS
............................
259
F.5
SOBOLEV
ESTIMATES
......................................................................................
262
G
VERIFICATION
OF
FERMI
S
GOLDEN
RULE
................................................................
269
G.1
REDUCTIONS
................................................................................................
269
G.2
PROOF
OF
THE
NON-VANISHING
OF
F2(V2)
....................................................
270
CONTENTS
IX
REFERENCES
..................................................................................................................
273
LIST
OF
NOTATION
........................................................................................................
279
|
| adam_txt |
CONTENTS
1
INTRODUCTION
.
1
1.1
LONG
TIME
EXISTENCE
FOR
PERTURBED
EVOLUTION
EQUATIONS
.
1
1.2
THE
USE
OF
DISPERSION
.
2
1.3
VECTOR
FIELDS
METHODS
AND
GLOBAL
SOLUTIONS
.
3
1.4
KLAINERMAN-SOBOLEV
ESTIMATES
IN
ONE
DIMENSION
.
6
1.5
THE
CASE
OF
LONG
RANGE
NONLINEARITIES
.
9
1.6
MORE
GENERAL
NONLINEARITIES
AND
NORMAL
FORMS
.
15
1.7
PERTURBATIONS
OF
NON-ZERO
STATIONARY
SOLUTION
.
21
1.8
THE
KINK
PROBLEM.
I
.
24
1.9
THE
KINK
PROBLEM
II.
COUPLING
WITH
THE
BOUND
STATE
.
27
2
THE
KINK
PROBLEM
.
31
2.1
STATEMENT
OF
THE
MAIN
RESULT
.
31
2.2
REDUCED
SYSTEM
.
33
2.3
STEP
1:
WRITING
OF
THE
SYSTEM
FROM
MULTILINEAR
OPERATORS
.
37
2.4
STEP
2:
FIRST
QUADRATIC
NORMAL
FORM
.
37
2.5
STEP
3:
APPROXIMATE
SOLUTION
.
38
2.6
STEP
4:
REDUCED
FORM
OF
DISPERSIVE
EQUATION
.
41
2.7
STEP
5:
NORMAL
FORMS
.
43
2.8
STEP
6:
BOOTSTRAP
OF
L
2
ESTIMATES
.
46
2.9
STEP
7:
BOOTSTRAP
OF
L
ESTIMATES
AND
END
OF
PROOF
.
46
2.10
FURTHER
COMMENTS
.
47
3
FIRST
QUADRATIC
NORMAL
FORM
.
53
3.1
EXPRESSION
OF
THE
EQUATION
FROM
MULTILINEAR
OPERATORS
.
53
3.2
FIRST
QUADRATIC
NORMAL
FORM
.
56
4
CONSTRUCTION
OF
APPROXIMATE
SOLUTIONS
.
59
4.1
APPROXIMATE
SOLUTION
TO
THE
DISPERSIVE
EQUATION
.
59
4.2
ASYMPTOTIC
ANALYSIS
OF
THE
ODE
.
73
5
REDUCED
FORM
OF
DISPERSIVE
EQUATION
.
81
5.1
A
FIXED
POINT
THEOREM
.
81
5.2
REDUCTION
OF
THE
DISPERSIVE
EQUATION
.
87
6
NORMAL
FORMS
.
103
6.1
EXPRESSION
OF
THE
EQUATION
AS
A
SYSTEM
.
104
6.2
NORMAL
FORMS
.
108
VIII
CONTENTS
7
BOOTSTRAP:
2
ESTIMATES
.
117
7.1
ESTIMATES
FOR
CUBIC
AND
QUARTIC
TERMS
.
117
7.2
ESTIMATES
FOR
QUADRATIC
TERMS
.
122
7.3
HIGHER-ORDER
TERMS
.
124
8
L
ESTIMATES
AND
END
OF
BOOTSTRAP
.
139
8.1
L
ESTIMATES
.
139
8.2
BOOTSTRAP
OF
L
ESTIMATES
.
145
8.3
END
OF
BOOTSTRAP
ARGUMENT
.
152
A
SCATTERING
FOR
TIME
INDEPENDENT
POTENTIAL
.
155
A.1
STATEMENT
OF
MAIN
PROPOSITION
.
155
A.2
PROOF
OF
MAIN
PROPOSITION
.
157
B
(SEMICLASSICAL)
PSEUDO-DIFFERENTIAL
OPERATORS
.
165
B.1
CLASSES
OF
SYMBOLS
AND
THEIR
QUANTIZATION
.
166
B.2
SYMBOLIC
CALCULUS
.
169
C
BOUNDS
FOR
FORCED
LINEAR
KLEIN-GORDON
EQUATIONS
.
177
C.1
LINEAR
SOLUTIONS
TO
HALF-KLEIN-GORDON
EQUATIONS
.
177
C.2
ACTION
OF
LINEAR
AND
BILINEAR
OPERATORS
.
191
C.3
AN
EXPLICIT
COMPUTATION
.
199
D
ACTION
OF
MULTILINEAR
OPERATORS
ON
SOBOLEV
AND
HOLDER
SPACES
.
203
D.
1
ACTION
OF
QUANTIZATION
OF
NON-SPACE-DECAYING
SYMBOLS
.
204
D.2
ACTION
OF
QUANTIZATION
OF
SPACE
DECAYING
SYMBOLS
.
213
D.3
WEYL
CALCULUS
.
223
E
WAVE
OPERATORS
FOR
TIME
DEPENDENT
POTENTIALS
.
229
E.
1
STATEMENT
OF
THE
RESULT
.
229
E.2
TECHNICAL
LEMMAS
.
234
E.3
PROOF
OF
PROPOSITION
E.
1.3
.
247
F
DIVISION
LEMMAS
AND
NORMAL
FORMS
.
253
F.1
DIVISION
LEMMAS
.
253
F.2
COMMUTATION
RESULTS
.
255
F.3
NORMAL
FORMS
FOR
NON-CHARACTERISTIC
TERMS
.
258
F.4
QUADRATIC
NORMAL
FORMS
FOR
SPACE
DECAYING
SYMBOLS
.
259
F.5
SOBOLEV
ESTIMATES
.
262
G
VERIFICATION
OF
FERMI
'
S
GOLDEN
RULE
.
269
G.1
REDUCTIONS
.
269
G.2
PROOF
OF
THE
NON-VANISHING
OF
F2(V2)
.
270
CONTENTS
IX
REFERENCES
.
273
LIST
OF
NOTATION
.
279 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Delort, Jean-Marc 1961- Masmoudi, Nader 1974- |
| author_GND | (DE-588)1027794106 (DE-588)1202473091 |
| author_facet | Delort, Jean-Marc 1961- Masmoudi, Nader 1974- |
| author_role | aut aut |
| author_sort | Delort, Jean-Marc 1961- |
| author_variant | j m d jmd n m nm |
| building | Verbundindex |
| bvnumber | BV048597861 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)1327677567 (DE-599)DNB1259073688 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048597861 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:09:11Z |
| indexdate | 2024-07-10T09:42:34Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470204 3985470200 9783985475209 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033973454 |
| oclc_num | 1327677567 |
| open_access_boolean | |
| owner | DE-188 DE-11 DE-83 |
| owner_facet | DE-188 DE-11 DE-83 |
| physical | ix, 280 Seiten Illustrationen 24 cm x 17 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | EMS Press |
| record_format | marc |
| series | Memoirs of the European Mathematical Society |
| series2 | Memoirs of the European Mathematical Society |
| spelling | Delort, Jean-Marc 1961- (DE-588)1027794106 aut Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations Jean-Marc Delort ; Nader Masmoudi Berlin EMS Press [2022] © 2022 ix, 280 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier Memoirs of the European Mathematical Society Vol. 1 Störungstheorie (DE-588)4128420-3 gnd rswk-swf Knicksoliton (DE-588)4245710-5 gnd rswk-swf Normalform (DE-588)4172025-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Dimension 1 (DE-588)4323094-5 gnd rswk-swf Klein-Gordon-Gleichung (DE-588)4164132-2 gnd rswk-swf kink nonlinear Klein–Gordon equations normal forms Fermi’s golden rule Wellengleichung (DE-588)4065315-8 s Dimension 1 (DE-588)4323094-5 s Knicksoliton (DE-588)4245710-5 s Klein-Gordon-Gleichung (DE-588)4164132-2 s Störungstheorie (DE-588)4128420-3 s Normalform (DE-588)4172025-8 s DE-604 Masmoudi, Nader 1974- (DE-588)1202473091 aut European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-520-9 Memoirs of the European Mathematical Society Vol. 1 (DE-604)BV048400142 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Delort, Jean-Marc 1961- Masmoudi, Nader 1974- Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations Memoirs of the European Mathematical Society Störungstheorie (DE-588)4128420-3 gnd Knicksoliton (DE-588)4245710-5 gnd Normalform (DE-588)4172025-8 gnd Wellengleichung (DE-588)4065315-8 gnd Dimension 1 (DE-588)4323094-5 gnd Klein-Gordon-Gleichung (DE-588)4164132-2 gnd |
| subject_GND | (DE-588)4128420-3 (DE-588)4245710-5 (DE-588)4172025-8 (DE-588)4065315-8 (DE-588)4323094-5 (DE-588)4164132-2 |
| title | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |
| title_auth | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |
| title_exact_search | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |
| title_exact_search_txtP | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |
| title_full | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations Jean-Marc Delort ; Nader Masmoudi |
| title_fullStr | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations Jean-Marc Delort ; Nader Masmoudi |
| title_full_unstemmed | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations Jean-Marc Delort ; Nader Masmoudi |
| title_short | Long-time dispersive estimates for perturbations of a kink solution of one-dimensional cubic wave equations |
| title_sort | long time dispersive estimates for perturbations of a kink solution of one dimensional cubic wave equations |
| topic | Störungstheorie (DE-588)4128420-3 gnd Knicksoliton (DE-588)4245710-5 gnd Normalform (DE-588)4172025-8 gnd Wellengleichung (DE-588)4065315-8 gnd Dimension 1 (DE-588)4323094-5 gnd Klein-Gordon-Gleichung (DE-588)4164132-2 gnd |
| topic_facet | Störungstheorie Knicksoliton Normalform Wellengleichung Dimension 1 Klein-Gordon-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973454&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV048400142 |
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