Type II blow up manifolds for the energy supercritical semilinear wave equation:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
March 2018
|
| Series: | Memoirs of the American Mathematical Society
volume 252, number 1205 (sixth of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 163, 4 ungezählte Seiten |
| ISBN: | 9781470428136 |
Staff View
MARC
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| 245 | 1 | 0 | |a Type II blow up manifolds for the energy supercritical semilinear wave equation |c Charles Collot |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. The Semilinear Wave Equation. 1
1.2. Blow up for (NLW) 1
1.3. Statement of the Result 3
1.4. Strategy of the Proof 8
Chapter 2. The Linearized Dynamics and the Construction of the
Approximate Blow up Profile 13
2.1. The Stationary State and its Numerology 13
2.2. Factorization of C 14
2.3. Inverting H on Radially Symmetric Functions 15
2.4. Adapted Derivatives, Admissible and Homogeneous Functions 16
2.5. Slowly Modulated Blow up Profiles and Growing Tails 20
2.6. Study of the Dynamical System Driving the Evolution of the
Parameters (5*)i i x, 30
Chapter 3. The Trapped Regime 35
3.1. Setting up the Bootstrap 35
3.1.1. Projection onto the Approximate Solutions Manifold 36
3.1.2. Modulation 37
3.1.3. Adapted Norms 38
3.1.4. Estimates of the Bootstrap and Main Proposition 39
3.2. Evolution Equations for e and w 41
3.3. Modulation Equations 42
3.4. Improved Modulation Equation for bl 44
3.5. Lyapunov Mono tonicity for the Low Sobolev Norm 48
3.6. Lyapunov Monotonicity for the High Sobolev Norm 52
3.7. Control from a Morawetz Type Quantity 63
Chapter 4. End of the Proof 69
4.1. End of the Proof of Proposition 3.2 69
4.2. Behavior of Sobolev Norms near Blow up Time 77
Chapter 5. Lipschitz Aspect and Codimension of the Set of Solutions
Described by Proposition 3.2 83
5.1. Lipschitz Dependence of the Unstable Modes under Extra Assumptions 84
5.1.1. Adapted Time for Comparison, Notations and Identities 85
5.1.2. Modulation Equations for the Difference 87
5.1.3. Energy Identities for the Difference of Errors 99
iii
IV
CONTENTS
5.1.4. Study of the Coupled Dynamical System, End of the Proof of
Proposition (5.2) 117
5.2. Removal of Extra Assumptions, End of the Proof of Theorem 5.1 124
5.2.1. Lower Order Decomposition 125
Appendix A. Properties of the Stationary State 139
Appendix B. Equivalence of Norms 143
Appendix C. Hardy Inequalities 147
Appendix D. Coercivity of the Adapted Norms 151
Appendix E. Specific Bounds for the Analysis 159
Acknowledgment 160
Bibliography 161
Index of the Constants 163
|
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| id | DE-604.BV044905958 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:04:23Z |
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| isbn | 9781470428136 |
| language | English |
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| publishDate | 2018 |
| publishDateSearch | 2018 |
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| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Collot, Charles aut Type II blow up manifolds for the energy supercritical semilinear wave equation Charles Collot Providence, Rhode Island American Mathematical Society March 2018 © 2018 v, 163, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 252, number 1205 (sixth of 6 numbers) Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Memoirs of the American Mathematical Society volume 252, number 1205 (sixth of 6 numbers) (DE-604)BV008000141 1205 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030299629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Collot, Charles Type II blow up manifolds for the energy supercritical semilinear wave equation Memoirs of the American Mathematical Society Mannigfaltigkeit (DE-588)4037379-4 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4065315-8 |
| title | Type II blow up manifolds for the energy supercritical semilinear wave equation |
| title_auth | Type II blow up manifolds for the energy supercritical semilinear wave equation |
| title_exact_search | Type II blow up manifolds for the energy supercritical semilinear wave equation |
| title_full | Type II blow up manifolds for the energy supercritical semilinear wave equation Charles Collot |
| title_fullStr | Type II blow up manifolds for the energy supercritical semilinear wave equation Charles Collot |
| title_full_unstemmed | Type II blow up manifolds for the energy supercritical semilinear wave equation Charles Collot |
| title_short | Type II blow up manifolds for the energy supercritical semilinear wave equation |
| title_sort | type ii blow up manifolds for the energy supercritical semilinear wave equation |
| topic | Mannigfaltigkeit (DE-588)4037379-4 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Mannigfaltigkeit Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030299629&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT collotcharles typeiiblowupmanifoldsfortheenergysupercriticalsemilinearwaveequation |