Caustics for dissipative semilinear oscillations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2000
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
685 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 144, Number 685 (third of 5 numbers) |
| Physical Description: | VIII, 72 S. graph. Darst. |
| ISBN: | 0821820419 |
Staff View
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| 245 | 1 | 0 | |a Caustics for dissipative semilinear oscillations |c Jean-Luc Joly ; Guy Metivier ; Jeffrey Rauch |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c 2000 | |
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Record in the Search Index
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| adam_text | Contents
1. Introduction 1
2. Notations and main results 5
2.1. The time evolution
2.2. Lagrangians, caustics and phases
2.3. IP estimates of oscillatory integrals
2.4. Oscillations and profiles
2.5. Sketch of the main results
2.6. Remarks and examples
3. Lp estimates for oscillatory integrals 17
3.1. Statement of the main estimate
3.2. Proof of Theorem 3.1.1
3.3. Proof of Theorem 3.1.2
3.4. Proof of Theorem 3.1.3.
3.5. Subcritical Lp estimates for Ie(A)
4. Oscillations and profiles 31
4.1. Estimates for Je(A) and Ie(A)
4.2. Extension to nonsmooth profiles
4.3. Weak profiles
5. The nonlinear interaction operators 39
5.1. The interaction operators for profiles
5.2. Profiles of nonlinear functions of oscillations
6. Proof of asymptotics 45
6.1. Weak convergence
6.2. Construction of approximate solutions
6.3. Strong convergences
6.4. Uniqueness for the profile equations
6.5. The main result
6.6. Absorption at supercritical points
6.7. Angular smoothness for profiles
7. Additional results and remarks 61
7.1. The wave equation
7.2. Lipschitzean nonlinearities and nonstrictly monotone nonlinearities
7.3. Nonlinear interaction and transfer of singularities above the caustic
8. References 71
vii
|
| any_adam_object | 1 |
| author | Joly, Jean-Luc 1942- Métivier, Guy Rauch, Jeffrey 1945- |
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| author_facet | Joly, Jean-Luc 1942- Métivier, Guy Rauch, Jeffrey 1945- |
| author_role | aut aut aut |
| author_sort | Joly, Jean-Luc 1942- |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:39:39Z |
| institution | BVB |
| isbn | 0821820419 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008949175 |
| oclc_num | 42823840 |
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| physical | VIII, 72 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Joly, Jean-Luc 1942- Verfasser (DE-588)1146260954 aut Caustics for dissipative semilinear oscillations Jean-Luc Joly ; Guy Metivier ; Jeffrey Rauch Providence, Rhode Island American Mathematical Society 2000 VIII, 72 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 685 Volume 144, Number 685 (third of 5 numbers) Differentiaalvergelijkingen gtt Equacoes diferenciais parciais larpcal Hyperbolische differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Numerieke methoden gtt Differential equations, Hyperbolic Numerical solutions Differential equations, Nonlinear Numerical solutions Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s Métivier, Guy Verfasser (DE-588)14122259X aut Rauch, Jeffrey 1945- Verfasser (DE-588)172326001 aut American Mathematical Society: Memoirs of the American Mathematical Society 685 (DE-604)BV008000141 685 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008949175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joly, Jean-Luc 1942- Métivier, Guy Rauch, Jeffrey 1945- Caustics for dissipative semilinear oscillations American Mathematical Society: Memoirs of the American Mathematical Society Differentiaalvergelijkingen gtt Equacoes diferenciais parciais larpcal Hyperbolische differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Numerieke methoden gtt Differential equations, Hyperbolic Numerical solutions Differential equations, Nonlinear Numerical solutions Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4205536-2 (DE-588)4131213-2 (DE-588)4128130-5 |
| title | Caustics for dissipative semilinear oscillations |
| title_auth | Caustics for dissipative semilinear oscillations |
| title_exact_search | Caustics for dissipative semilinear oscillations |
| title_full | Caustics for dissipative semilinear oscillations Jean-Luc Joly ; Guy Metivier ; Jeffrey Rauch |
| title_fullStr | Caustics for dissipative semilinear oscillations Jean-Luc Joly ; Guy Metivier ; Jeffrey Rauch |
| title_full_unstemmed | Caustics for dissipative semilinear oscillations Jean-Luc Joly ; Guy Metivier ; Jeffrey Rauch |
| title_short | Caustics for dissipative semilinear oscillations |
| title_sort | caustics for dissipative semilinear oscillations |
| topic | Differentiaalvergelijkingen gtt Equacoes diferenciais parciais larpcal Hyperbolische differentiaalvergelijkingen gtt Niet-lineaire vergelijkingen gtt Numerieke methoden gtt Differential equations, Hyperbolic Numerical solutions Differential equations, Nonlinear Numerical solutions Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differentiaalvergelijkingen Equacoes diferenciais parciais Hyperbolische differentiaalvergelijkingen Niet-lineaire vergelijkingen Numerieke methoden Differential equations, Hyperbolic Numerical solutions Differential equations, Nonlinear Numerical solutions Nichtlineare Differentialgleichung Hyperbolische Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008949175&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT jolyjeanluc causticsfordissipativesemilinearoscillations AT metivierguy causticsfordissipativesemilinearoscillations AT rauchjeffrey causticsfordissipativesemilinearoscillations |