Hyperbolic equations and frequency interactions:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1999
|
| Schriftenreihe: | Park City Mathematics Institute: IAS Park City Mathematics Series
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 466 S. graph. Darst. |
| ISBN: | 0821805924 |
Internformat
MARC
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| 245 | 1 | 0 | |a Hyperbolic equations and frequency interactions |c Luis Caffarelli ... ed. |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1999 | |
| 300 | |a XII, 466 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Park City Mathematics Institute: IAS Park City Mathematics Series |v 5 | |
| 650 | 0 | 7 | |a Hyperbolische Differentialgleichung |0 (DE-588)4131213-2 |2 gnd |9 rswk-swf |
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| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1995 |z Park City Utah |2 gnd-content | |
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| 700 | 1 | |a Caffarelli, Luis A. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804127333812011008 |
|---|---|
| adam_text | Contents
Preface xi
Introduction 1
Jean Bourgain, Nonlinear Schrodinger Equations 3
Introduction 5
Lecture 1. Generalities and Initial Value Problems 7
Comments and references related to Lecture 1 14
Lecture 2. The Initial Value Problem (continued) 15
Proof of Theorem 1.36 20
Comments on the proofs of Theorems 1.37, 1.40, 1.41 25
Addition to Lecture 2, Remarks on the growth of higher Sobolev norms 29
Comments and references related to Lecture 2 33
Lecture 3. A Digression: The Initial Value Problem for the KdV Equation 35
Comments and references related to Lecture 3 40
Lecture 4. ID Invariant Gibbs Measures 41
Comments and references related to Lecture 4 49
Lecture 5. Invariant Measures (2D) 51
Comments and references related to Lecture 5 67
Lecture 6. Quasi Periodic Solutions of Hamiltonian PDE 69
Introduction 69
Comments 84
Some references related to Lecture 6 85
Lecture 7. Time Periodic Solutions 87
Comments and references related to Lecture 7 100
Lecture 8. Time Quasi Periodic Solutions 101
Further comments 113
References and comments 116
Lecture 9. Normal Forms 117
Reference 126
Lecture 10. Applications of Symplectic Capacities to Hamiltonian PDE 127
Comments and references related to Lecture 10 138
V
vi CONTENTS
Appendix 141
Remarks on longtime behaviour of the flow of Hamiltonian PDE 141
References to Appendix 157
Ingrid C. Daubechies and Anna C. Gilbert, Harmonic Analysis,
Wavelets and Applications 159
Lecture 1. Introduction 161
Lecture 2. Constructing Orthonormal Wavelet Bases: Multiresolution
Analysis 169
Lecture 3. Wavelet Bases: Construction and Algorithms 175
Lecture 4. More Wavelet Bases 183
Lecture 5. Wavelets in Other Functional Spaces 191
Lecture 6. Pointwise Convergence for Wavelet Expansions 199
Lecture 7. Two Dimensional Wavelets and Operators 205
Lecture 8. Wavelets and Differential Equations 215
References 225
Susan Friedlander, Lectures on Stability and Instability of an Ideal
Fluid 227
Introduction 229
Lecture 1. Equations of Motion 233
1.1. Ideal fluid model 233
1.2. Euler equations 234
1.3. Lagrangian trajectories and streamlines 235
1.4. Vorticity 235
Lecture 2. Initial Boundary Value Problem 237
2.1. Existence and uniqueness theorems 238
2.2. Navier Stokes equations 239
Lecture 3. The Type of the Euler Equations 241
3.1. Linearized Euler equations 241
3.2. Computation of principal symbol 241
3.3. Wave motion supported by linearized Euler equations 244
Lecture 4. Vorticity 247
4.1. Vorticity and stream function in two dimensions 248
4.2. Extra complications in three dimensions 250
4.3. Vorticity theorems 250
4.4. Helmholtz Vortex Theorems 252
4.5. Role of vorticity in PDE theory of Euler equations 255
Lecture 5. Steady Flows 257
CONTENTS vii
5.1. Two dimensional case 257
5.2. Three dimensional case 258
Lecture 6. Stability/Instability of an Equilibrium State 263
6.1. Linear stability (instability) 263
6.2. Nonlinear (Lyapunov) stability 265
Lecture 7. Two Dimensional Spectral Problem 267
Lecture 8. Arnold Criterion for Nonlinear Stability 271
Lecture 9. Plane Parallel Shear Flow 273
Lecture 10. Instability in a Vorticity Norm 277
Lecture 11. Sufficient Condition for Instability 279
Lecture 12. Exponential Stretching 285
Lecture 13. Integrable Flows 289
Lecture 14. Baroclinic Instability 291
Lecture 15. Nonlinear Instability 295
Conclusion 296
References 299
George Papanicolaou and Leonid Ryzhik, Waves and Transport 305
Lecture 1. Introduction 307
1.1. The geophysical problem 307
1.2. Radiative transport equations 309
1.3. Transport theory for electromagnetic waves 311
1.4. Transport theory for elastic waves 313
1.5. Brief outline 316
Lecture 2. The Schrodinger Equation 317
2.1. The Schrodinger equation 317
2.2. Standard high frequency asymptotics 318
2.3. The Wigner distribution 320
2.4. General properties of the Wigner distribution 322
2.5. Convergence of energy 325
Lecture 3. Symmetric Hyperbolic Systems 327
3.1. General symmetric hyperbolic systems 327
3.2. High frequency approximation for acoustic waves 332
3.3. Geometrical optics for electromagnetic waves 336
3.4. High frequency approximation for elastic waves 338
Lecture 4. Waves in Random Media 343
4.1. The Schrodinger equation 343
4.2. Transport equations without polarization 346
4.3. Transport equations with polarization 350
viii CONTENTS
4.4. Transport equations for acoustic waves 351
4.5. Transport equations for electromagnetic waves 351
4.6. Transport equations for elastic waves 353
Lecture 5. The Diffusion Approximation 359
5.1. Diffusion approximation for acoustic waves 359
5.2. Diffusion approximation for electromagnetic waves 362
5.3. Diffusion approximation for elastic waves 363
Lecture 6. The Geophysical Applications 367
6.1. Introduction 367
6.2. Radiative transport equations 368
6.3. Transport theory for elastic waves 371
6.4. Summary 377
References 379
Jeffrey Rauch with the assistance of Markus Keel, Lectures on
Geometric Optics 383
Lecture 1. Introduction 385
Lecture 2. Basic Linear Existence Theorems 389
2.1. Energy estimates for symmetric hyperbolic systems 389
2.2. Existence theorems for symmetric hyperbolic systems 393
2.3. Finite speed of propagation 395
2.4. Plane waves, characteristic variety and finite speed 397
2.5. Solutions on cones of determinacy 399
Lecture 3. Examples of Propagation of Singularities and of Energy 401
3.1. Examples 402
Lecture 4. Elliptic Geometric Optics 407
4.1. Constant coefficients and linear phases 407
4.2. Iterative improvement for variable coefficients and nonlinear phases 408
4.3. Formal asymptotics approach 410
4.4. Perturbation approach 413
4.5. Elliptic Regularity Theorem 414
Lecture 5. Linear Hyperbolic Geometric Optics 417
5.1. Constant coefficients and linear phases 417
5.2. Scalar constant coefficient operators and linear phases 419
5.3. Variable coefficient systems and nonlinear phases 420
5.4. Rays and transport 427
Lecture 6. Basic Nonlinear Existence Theorems 431
6.1. Introduction 431
6.2. Schauder s Lemma and Sobolev Embedding 432
6.3. Basic existence theorem 436
6.4. Moser s inequality and the nature of the breakdown 438
CONTENTS ix
Lecture 7. One Phase Nonlinear Geometric Optics 441
7.1. Amplitudes and harmonics 441
7.2. More on the generation of harmonics 444
7.3. Formulating the ansatz 445
7.4. Equations for the profiles 446
7.5. Solving the profile equations 449
7.6. Rays and nonlinear transport 453
Lecture 8. Justification of One Phase Nonlinear Geometric Optics 457
8.1. The spaces H*(Rd) 457
8.2. H* estimates for linear symmetric hyperbolic systems 460
8.3. Justification of the nonlinear asymptotics 461
References 465
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| id | DE-604.BV012673399 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:41Z |
| institution | BVB |
| isbn | 0821805924 |
| language | English |
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| physical | XII, 466 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | American Math. Soc. |
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| series | Park City Mathematics Institute: IAS Park City Mathematics Series |
| series2 | Park City Mathematics Institute: IAS Park City Mathematics Series |
| spelling | Hyperbolic equations and frequency interactions Luis Caffarelli ... ed. Providence, RI American Math. Soc. 1999 XII, 466 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Park City Mathematics Institute: IAS Park City Mathematics Series 5 Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1995 Park City Utah gnd-content Hyperbolische Differentialgleichung (DE-588)4131213-2 s Wellengleichung (DE-588)4065315-8 s DE-604 Caffarelli, Luis A. Sonstige oth Park City Mathematics Institute: IAS Park City Mathematics Series 5 (DE-604)BV010402400 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008612695&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hyperbolic equations and frequency interactions Park City Mathematics Institute: IAS Park City Mathematics Series Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4131213-2 (DE-588)4065315-8 (DE-588)1071861417 |
| title | Hyperbolic equations and frequency interactions |
| title_auth | Hyperbolic equations and frequency interactions |
| title_exact_search | Hyperbolic equations and frequency interactions |
| title_full | Hyperbolic equations and frequency interactions Luis Caffarelli ... ed. |
| title_fullStr | Hyperbolic equations and frequency interactions Luis Caffarelli ... ed. |
| title_full_unstemmed | Hyperbolic equations and frequency interactions Luis Caffarelli ... ed. |
| title_short | Hyperbolic equations and frequency interactions |
| title_sort | hyperbolic equations and frequency interactions |
| topic | Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Hyperbolische Differentialgleichung Wellengleichung Konferenzschrift 1995 Park City Utah |
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