Semilinear Schrödinger equations
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| Format: | Buch |
| Sprache: | English |
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New York, NY
Courant Inst. of Math. Sciences [u.a.]
2003
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| Schriftenreihe: | Courant lecture notes in mathematics
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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MARC
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| 100 | 1 | |a Cazenave, Thierry |d 1954- |e Verfasser |0 (DE-588)130600016 |4 aut | |
| 245 | 1 | 0 | |a Semilinear Schrödinger equations |c Thierry Cazenave |
| 264 | 1 | |a New York, NY |b Courant Inst. of Math. Sciences [u.a.] |c 2003 | |
| 300 | |a XIII, 323 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Courant lecture notes in mathematics |v 10 | |
| 650 | 4 | |a Schrödinger equation | |
| 650 | 0 | 7 | |a Semilineare Differentialgleichung |0 (DE-588)4180958-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |D s |
| 689 | 0 | 1 | |a Semilineare Differentialgleichung |0 (DE-588)4180958-0 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010441293 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 941 |
|---|---|
| DE-BY-TUM_katkey | 1868527 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071421711 |
| _version_ | 1820896890942652416 |
| adam_text | Contents
Preface vii
Notation ix
1. Preliminary Results 1
1.1. Functional Analysis 1
1.2. Integration 3
1.3. Sobolev Spaces 6
1.4. Sobolev and Besov Spaces onR 12
1.5. Elliptic Equations 15
1.6. Semigroups of Linear Operators 18
1.7. Some Compactness Tools 20
2. The Linear Schrodinger Equation 29
2.1. Basic Properties 29
2.2. Fundamental Properties in R^ 30
2.3. Strichartz s Estimates 33
2.4. Strichartz s Estimates for Nonadmissible Pairs 40
2.5. Space Decay and Smoothing Effect in K^ 41
2.6. Homogeneous Data in RN 43
2.7. Comments 51
3. The Cauchy Problem in a General Domain 55
3.1. The Notion of Solution 55
3.2. Some Typical Nonlinearities 58
3.3. Local Existence in the Energy Space 63
3.4. Energy Estimates and Global Existence 74
3.5. The Nonlinear Schrodinger Equation in One Dimension .... 77
3.6. The Nonlinear Schrodinger Equation in Two Dimensions .... 78
3.7. Comments 80
4. The Local Cauchy Problem 83
4.1. Outline 83
4.2. Strichartz s Estimates and Uniqueness 84
4.3. Local Existence in H1 (RN) 92
4.4. Kato s Method 93
4.5. A Critical Casein i/^R^) 103
4.6. L2 Solutions 109
4.7. A Critical Case in L2(RN) 115
4.8. H2 Solutions 119
4.9. Hs Solutions, s N/2 125
4.10. Hm Solutions, m N/2 134
v
vi CONTENTS
4.11. The Cauchy Problem for a Nonautonomous Schrodinger
Equation 138
4.12. Comments 143
5. Regularity and the Smoothing Effect 147
5.1. Hs Regularity, 0 s min{l, iV/2} 147
5.2. H1 Regularity 149
5.3. H2 Regularity 152
5.4. Hm Regularity, m N/2 154
5.5. Arbitrary Regularity 155
5.6. The C°° Smoothing Effect 156
5.7. Comments 160
6. Global Existence and Finite-Time Blowup 163
6.1. Energy estimates and Global Existence 163
6.2. Global Existence for Small Data 165
6.3. Global Existence for Oscillating Data 167
6.4. Global Existence for Asymptotically Homogeneous Initial Data . 171
6.5. Finite-Time Blowup 178
6.6. The Critical Case: Sharp Existence and Blowup Results .... 196
6.7. The Pseudoconformal Transformation and Applications 204
6.8. Comments 208
7. Asymptotic Behavior in the Repulsive Case 211
7.1. Basic Notions of Scattering Theory 211
7.2. The Pseudoconformal Conservation Law 213
7.3. Decay of Solutions in the Weighted L2 Space 215
7.4. Scattering Theory in the Weighted L2 Space 220
7.5. Applications of the Pseudoconformal Transformation 224
7.6. Morawetz s Estimate 233
7.7. Decay of Solutions in the Energy Space 239
7.8. Scattering Theory in the Energy Space 246
7.9. Comments 249
8. Stability of Bound States in the Attractive Case 255
8.1. Nonlinear Bound States 255
8.2. An Instability Result 269
8.3. A Stability Result 274
8.4. Comments 280
9. Further Results 283
9.1. The Nonlinear Schrodinger Equation with a Magnetic Field . . 283
9.2. The nonlinear Schrodinger Equation with a Quadratic Potential . 287
9.3. The Logarithmic Schrodinger Equation 291
9.4. Existence of Weak Solutions for Large Nonlinearities 299
9.5. Comments 303
Bibliography 305
|
| any_adam_object | 1 |
| author | Cazenave, Thierry 1954- |
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| author_facet | Cazenave, Thierry 1954- |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV017321206 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.26.W28 |
| callnumber-search | QC174.26.W28 |
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| callnumber-subject | QC - Physics |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)52554437 (DE-599)BVBBV017321206 |
| dewey-full | 530.12/4 530.124 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 530.124 |
| dewey-search | 530.12/4 530.124 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-23T16:19:52Z |
| institution | BVB |
| isbn | 0821833995 9780821833995 |
| language | English |
| lccn | 2003057905 |
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| physical | XIII, 323 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Courant Inst. of Math. Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spellingShingle | Cazenave, Thierry 1954- Semilinear Schrödinger equations Courant lecture notes in mathematics Schrödinger equation Semilineare Differentialgleichung (DE-588)4180958-0 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd |
| subject_GND | (DE-588)4180958-0 (DE-588)4053332-3 |
| title | Semilinear Schrödinger equations |
| title_auth | Semilinear Schrödinger equations |
| title_exact_search | Semilinear Schrödinger equations |
| title_full | Semilinear Schrödinger equations Thierry Cazenave |
| title_fullStr | Semilinear Schrödinger equations Thierry Cazenave |
| title_full_unstemmed | Semilinear Schrödinger equations Thierry Cazenave |
| title_short | Semilinear Schrödinger equations |
| title_sort | semilinear schrodinger equations |
| topic | Schrödinger equation Semilineare Differentialgleichung (DE-588)4180958-0 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd |
| topic_facet | Schrödinger equation Semilineare Differentialgleichung Schrödinger-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441293&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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