Introduction to nonlinear dispersive equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 256 S. |
| ISBN: | 9780387848983 |
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Record in the Search Index
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| adam_text | FELIPE LINARES * GUSTAVO PONCE INTRODUCTION TO NONLINEAR DISPERSIVE
EQUATIONS 4Y SPRIN GER CONTENTS THE FOURIER TRANSFORM 1 1.1 THE FOURIER
TRANSFORM IN L 1 (K ) 1 1.2 THE FOURIER TRANSFORM IN L 2 (K ) 6 1.3
TEMPERED DISTRIBUTIONS 8 1.4 OSCILLATORY INTEGRALS IN ONE DIMENSION 13
1.5 APPLICATIONS 17 1.6 EXERCISES 18 INTERPOLATION OF OPERATORS. A
MULTIPLIER THEOREM 25 2.1 THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1
APPLICATIONS 28 2.2 MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1
APPLICATIONS 33 2.3 THE STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER
THEOREM 38 2.5 EXERCISES 39 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL
OPERATORS 45 3.1 BASICS 45 3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE
BICHARACTERISTIC FLOW 53 3.4 EXERCISES 55 THE LINEAR SCHROEDINGER
EQUATION 59 4. 1 BASIC RESULTS 59 4.2 GLOBAL SMOOTHING EFFECTS 64 4.3
LOCAL SMOOTHING EFFECTS 67 4.4 COMMENTS 72 4.5 EXERCISES 84 CONTENTS 1
THE FOURIER TRANSFORM 1 1 .1 THE FOURIER TRANSFORM IN L) (R N ) 1 1.2
THE FOURIER TRANSFORM IN L 2 (M ) 6 1.3 TEMPERED DISTRIBUTIONS 8 1.4
OSCILLATORY INTEGRALS IN ONE DIMENSION 13 1.5 APPLICATIONS 17 1.6
EXERCISES 18 2 INTERPOLATION OF OPERATORS. A MULTIPLIER THEOREM 25 2.1
THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1 APPLICATIONS 28 2.2
MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1 APPLICATIONS 33 2.3 THE
STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER THEOREM 38 2.5 EXERCISES
39 3 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL OPERATORS 45 3.1 BASICS 45
3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE BICHARACTERISTIC FLOW 53 3.4
EXERCISES 55 4 THE LINEAR SCHRODINGER EQUATION 59 4.1 BASIC RESULTS 59
4.2 GLOBAL SMOOTHING EFFECTS 64 4.3 LOCAL SMOOTHING EFFECTS 67 4.4
COMMENTS 72 4.5 EXERCISES 84 IX X CONTENTS 5 THE NONLINEAR SCHROEDINGER
EQUATION. LOCAL THEORY 89 5.1 L 2 THEORY 91 5.2 H 1 THEORY 99 5.3 H 2
THEORY 103 5.4 COMMENTS 106 5.5 EXERCISES 116 6 ASYMPTOTIC BEHAVIOR FOR
NLS EQUATION 119 6.1 GLOBAL RESULTS 119 6.2 FORMATION OF SINGULARITIES
124 6.2.1 CASE A G (1 +4/N,L + 4/(-2)) 126 6.2.2 CASE A = 1 +4/N 128
6.3 COMMENTS 133 6.4 EXERCISES 137 7 KORTEWEG-DE VRIES EQUATION 139 7.1
LINEAR PROPERTIES 141 7.2 MODIFIED KORTEWEG-DE VRIES EQUATION 146 7.3
GENERALIZED KORTEWEG-DE VRIES EQUATION 149 7.4 KORTEWEG-DE VRIES
EQUATION 155 7.5 COMMENTS 166 7.6 EXERCISES 170 8 ASYMPTOTIC BEHAVIOR
FOR K-GKDV EQUATIONS 173 8.1 CASES K = 1,2,3 174 8.2 CASE * = 4 180 8.3
COMMENTS 185 8.4 EXERCISES 188 9 OTHER NONLINEAR DISPERSIVE MODELS 191
9. 1 DAVEY-STEWARTSON SYSTEMS 191 9.2 ISHIMORI EQUATION 193 9.3 KP
EQUATIONS 194 9.4 BO EQUATION 196 9.5 ZAKHAROV SYSTEM 200 9.6 HIGHER
ORDER KDV EQUATIONS 203 9.7 EXERCISES 208 10 GENERAL QUASILINEAR
SCHROEDINGER EQUATION 211 10.1 THE GENERAL QUASILINEAR SCHROEDINGER
EQUATION 211 10.2 COMMENTS 230 10.3 EXERCISES 231 A APPENDIX 233
REFERENCES 239 CONTENTS XI INDEX 255
|
| adam_txt |
FELIPE LINARES * GUSTAVO PONCE INTRODUCTION TO NONLINEAR DISPERSIVE
EQUATIONS 4Y SPRIN GER CONTENTS THE FOURIER TRANSFORM 1 1.1 THE FOURIER
TRANSFORM IN L 1 (K") 1 1.2 THE FOURIER TRANSFORM IN L 2 (K") 6 1.3
TEMPERED DISTRIBUTIONS 8 1.4 OSCILLATORY INTEGRALS IN ONE DIMENSION 13
1.5 APPLICATIONS 17 1.6 EXERCISES 18 INTERPOLATION OF OPERATORS. A
MULTIPLIER THEOREM 25 2.1 THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1
APPLICATIONS 28 2.2 MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1
APPLICATIONS 33 2.3 THE STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER
THEOREM 38 2.5 EXERCISES 39 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL
OPERATORS 45 3.1 BASICS 45 3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE
BICHARACTERISTIC FLOW 53 3.4 EXERCISES 55 THE LINEAR SCHROEDINGER
EQUATION 59 4. 1 BASIC RESULTS 59 4.2 GLOBAL SMOOTHING EFFECTS 64 4.3
LOCAL SMOOTHING EFFECTS 67 4.4 COMMENTS 72 4.5 EXERCISES 84 CONTENTS 1
THE FOURIER TRANSFORM 1 1 .1 THE FOURIER TRANSFORM IN L) (R N ) 1 1.2
THE FOURIER TRANSFORM IN L 2 (M") 6 1.3 TEMPERED DISTRIBUTIONS 8 1.4
OSCILLATORY INTEGRALS IN ONE DIMENSION 13 1.5 APPLICATIONS 17 1.6
EXERCISES 18 2 INTERPOLATION OF OPERATORS. A MULTIPLIER THEOREM 25 2.1
THE RIESZ-THORIN CONVEXITY THEOREM 25 2.1.1 APPLICATIONS 28 2.2
MARCINKIEWICZ INTERPOLATION THEOREM 29 2.2.1 APPLICATIONS 33 2.3 THE
STEIN INTERPOLATION THEOREM 37 2.4 A MULTIPLIER THEOREM 38 2.5 EXERCISES
39 3 SOBOLEV SPACES AND PSEUDO-DIFFERENTIAL OPERATORS 45 3.1 BASICS 45
3.2 PSEUDODIFFERENTIAL OPERATORS 51 3.3 THE BICHARACTERISTIC FLOW 53 3.4
EXERCISES 55 4 THE LINEAR SCHRODINGER EQUATION 59 4.1 BASIC RESULTS 59
4.2 GLOBAL SMOOTHING EFFECTS 64 4.3 LOCAL SMOOTHING EFFECTS 67 4.4
COMMENTS 72 4.5 EXERCISES 84 IX X CONTENTS 5 THE NONLINEAR SCHROEDINGER
EQUATION. LOCAL THEORY 89 5.1 L 2 THEORY 91 5.2 H 1 THEORY 99 5.3 H 2
THEORY 103 5.4 COMMENTS 106 5.5 EXERCISES 116 6 ASYMPTOTIC BEHAVIOR FOR
NLS EQUATION 119 6.1 GLOBAL RESULTS 119 6.2 FORMATION OF SINGULARITIES
124 6.2.1 CASE A G (1 +4/N,L + 4/(-2)) 126 6.2.2 CASE A = 1 +4/N 128
6.3 COMMENTS 133 6.4 EXERCISES 137 7 KORTEWEG-DE VRIES EQUATION 139 7.1
LINEAR PROPERTIES 141 7.2 MODIFIED KORTEWEG-DE VRIES EQUATION 146 7.3
GENERALIZED KORTEWEG-DE VRIES EQUATION 149 7.4 KORTEWEG-DE VRIES
EQUATION 155 7.5 COMMENTS 166 7.6 EXERCISES 170 8 ASYMPTOTIC BEHAVIOR
FOR K-GKDV EQUATIONS 173 8.1 CASES K = 1,2,3 174 8.2 CASE * = 4 180 8.3
COMMENTS 185 8.4 EXERCISES 188 9 OTHER NONLINEAR DISPERSIVE MODELS 191
9. 1 DAVEY-STEWARTSON SYSTEMS 191 9.2 ISHIMORI EQUATION 193 9.3 KP
EQUATIONS 194 9.4 BO EQUATION 196 9.5 ZAKHAROV SYSTEM 200 9.6 HIGHER
ORDER KDV EQUATIONS 203 9.7 EXERCISES 208 10 GENERAL QUASILINEAR
SCHROEDINGER EQUATION 211 10.1 THE GENERAL QUASILINEAR SCHROEDINGER
EQUATION 211 10.2 COMMENTS 230 10.3 EXERCISES 231 A APPENDIX 233
REFERENCES 239 CONTENTS XI INDEX 255 |
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| spelling | Linares, Felipe Verfasser aut Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce New York, NY Springer 2009 XI, 256 S. txt rdacontent n rdamedia nc rdacarrier Universitext Differential equations, Partial Nonlinear wave equations Wellengleichung (DE-588)4065315-8 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Wellengleichung (DE-588)4065315-8 s DE-604 Ponce, Gustavo Verfasser aut Erscheint auch als Online-Ausgabe 978-0-387-84899-0 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016991763&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Linares, Felipe Ponce, Gustavo Introduction to nonlinear dispersive equations Differential equations, Partial Nonlinear wave equations Wellengleichung (DE-588)4065315-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4065315-8 (DE-588)4128900-6 |
| title | Introduction to nonlinear dispersive equations |
| title_auth | Introduction to nonlinear dispersive equations |
| title_exact_search | Introduction to nonlinear dispersive equations |
| title_exact_search_txtP | Introduction to nonlinear dispersive equations |
| title_full | Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce |
| title_fullStr | Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce |
| title_full_unstemmed | Introduction to nonlinear dispersive equations Felipe Linares ; Gustavo Ponce |
| title_short | Introduction to nonlinear dispersive equations |
| title_sort | introduction to nonlinear dispersive equations |
| topic | Differential equations, Partial Nonlinear wave equations Wellengleichung (DE-588)4065315-8 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Differential equations, Partial Nonlinear wave equations Wellengleichung Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016991763&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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