Waves and boundary problems:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2018]
|
| Schriftenreihe: | Nonlinear equations with small parameter / Sergey G. Glebov
Volume 2 De Gruyter series in nonlinear analysis and applications Volume 23/2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVIII, 422 Seiten Illustrationen 25 cm, 865 g |
| ISBN: | 9783110533835 3110533839 |
Internformat
MARC
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| 245 | 1 | 0 | |a Waves and boundary problems |c Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| 264 | 1 | |a Berlin |b De Gruyter |c [2018] | |
| 300 | |a XVIII, 422 Seiten |b Illustrationen |c 25 cm, 865 g | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonlinear equations with small parameter / Sergey G. Glebov |v Volume 2 | |
| 490 | 0 | |a De Gruyter series in nonlinear analysis and applications |v Volume 23/2 | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 9783110533903 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |t Waves and Boundary Problems |b 1. Auflage |d Berlin/Boston : De Gruyter, 2018 |h Online-Ressource, 441 Seiten |
| 810 | 2 | |a Sergey G. Glebov |t Nonlinear equations with small parameter |v Volume 2 |w (DE-604)BV005530011 |9 23,2 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE * VII
INTRODUCTION * XV
1 THE SOLITARY WAVES GENERATION DUE TO PASSAGE THROUGH THE LOCAL
RESONANCE * 1
1.1 THE NONLINEAR SCHROEDINGER EQUATION. SCATTERING OF SOLITONS
ON RESONANCE * 1
1.1.1 PROBLEM STATEMENT AND RESULT* 3
1.1.2 INCIDENT WAVES * 4
1.1.3 SCATTERING * 6
1.1.4 SCATTERED WAVES * 8
1.1.5 NUMERICAL JUSTIFICATION OF ASYMPTOTIC ANALYSIS * 10
1.2 GENERATION OF SOLITARY PACKETS OF WAVES IN THE NONLINEAR
KLEIN-GORDON
EQUATION * 11
1.2.1 MAIN RESULT* 11
1.2.2 PRE-RESONANCE EXPANSION * 14
1.2.3 INTERNAL ASYMPTOTICS * 16
1.2.4 POST-RESONANCE EXPANSION * 23
1.3 THE PERTURBED KDV EQUATION AND PASSAGE THROUGH THE RESONANCE * 28
1.3.1 FORCED OSCILLATIONS * 29
1.3.2 INSIDE THE RESONANCE * 31
1.3.3 POST-RESONANCE EXPANSION * 37
1.3.4 NUMERICAL SIMULATIONS * 39
1.4 AUTO-RESONANT SOLITON AND PERTURBATION
WITH DECAYING AMPLITUDE * 40
1.4.1 JUSTIFICATION
-----
41
1.4.2 DERIVATION OF THE MODEL EQUATION FOR AUTO-RESONANCE * 42
1.4.3 AN ASYMPTOTIC SOLUTION OF THE MODEL EQUATION * 43
1.4.4 EFFECT OF DISSIPATION * 46
2 REGULAR PERTURBATION OF ILL-POSED PROBLEMS * 48
2.1 MIXED PROBLEMS WITH A PARAMETER * 49
2.1.1 PRELIMINARIES * 49
2.1.2 THE CAUCHY PROBLEM * 53
2.1.3 A PERTURBATION * 58
2.1.4 THE MAIN THEOREM * 62
2.1.5 THE WELL-POSED CASE * 65
2.1.6 ON FINDING THE SOLUTION * 67
2.1.7 DIRAC OPERATORS * 72
2.2 KERNEL SPIKES OF SINGULAR PROBLEMS * 76
2.2.1 SOFT EXPANSIONS
-----
77
2.2.2 HARMONIC EXTENSION * 79
2.2.3 AUXILIARY RESULTS * 80
2.2.4 FORMULAS FOR COEFFICIENTS * 81
2.2.5 LAURENT SERIES
-----
84
2.2.6 EXPANSION OF THE POISSON KERNEL * 85
2.3 AN ASYMPTOTIC EXPANSION OF THE MARTINELLI-BOCHNER INTEGRAL * 86
2.3.1 ASYMPTOTIC EXPANSION * 87
2.3.2 THE BOCHNER-MARTINELLI INTEGRAL
-----
88
2.3.3 REGULARIZATION * 94
2.3.4 PROOF OF THE THEOREM * 95
2.4 A FORMULA FOR THE NUMBER OF LATTICE POINTS IN A DOMAIN * 97
2.4.1 LOGARITHMIC RESIDUE FORMULA * 97
2.4.2 THE INTEGRAL FORMULA * 98
2.4.3 THE ONE-DIMENSIONAL CASE * 101
2.4.4 SOME COMMENTS * 102
3 ASYMPTOTICS AT CHARACTERISTIC POINTS * 103
3.1 ASYMPTOTIC SOLUTIONS OF THE ID HEAT EQUATION * 103
3.1.1 PRELIMINARIES * 103
3.1.2 ON THE HEAT EQUATION * 104
3.1.3 BLOW-UP TECHNIQUES * 106
3.1.4 FURTHER REDUCTION * 109
3.1.5 THE UNPERTURBED PROBLEM * 111
3.1.6 ASYMPTOTIC SOLUTIONS * 113
3.1.7 LOCAL SOLVABILITY AT A CUSP * 117
3.2 EULER THEORY ON A SPINDLE * 119
3.2.1 PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH CONICAL POINTS *
120
3.2.2 MEROMORPHIC FAMILIES * 122
3.2.3 CHARACTERISTIC VALUES
-----
123
3.2.4 FACTORIZATION
-----
126
3.2.5 RESOLVENT
-----
129
3.2.6 UNITARY REDUCTION * 130
3.2.7 INHOMOGENEOUS EQUATION * 133
3.2.8 TRANSPOSED EQUATIONS * 140
3.2.9 INDEX
-----
143
3.3 THE LAPLACE-BELTRAMI OPERATOR ON A ROTATIONALLY
SYMMETRIC SURFACE * 145
3.3.1 CALCULUS ON SINGULAR VARIETIES * 145
3.3.2 GEOMETRY * 146
3.3.3 LAPLACE-BELTRAMI OPERATOR * 148
3.3.4 WEIGHTED SPACES * 149
3.3.5 RESOLVENT * 151
3.3.6 FREDHOLM THEORY * 153
3.3.7 ASYMPTOTICS
-----
155
3.3.8 INDEX FORMULA * 156
3.4 BOUNDARY VALUE PROBLEMS FOR PARABOLIC EQUATIONS * 158
3.4.1 ANISOTROPIC ELLIPTICITY * 161
3.4.2 PARABOLICITY AFTER PETROVSKII * 162
3.4.3 CHARACTERISTIC POINTS * 163
3.4.4 WEIGHTED SPACES * 166
3.4.5 SOLUTION IN A SPECIAL DOMAIN * 174
3.4.6 LOCAL PARAMETRICES * 182
3.4.7 THE GLOBAL PARAMETRIX * 192
3.4.8 REGULARITY OF SOLUTIONS * 206
3.4.9 SOME PARTICULAR CASES * 210
4 ASYMPTOTIC EXPANSIONS OF SINGULAR PERTURBATION THEORY * 214
4.1 SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS * 214
4.1.1 WHITE NOISE PERTURBATION OF DYNAMICAL SYSTEMS * 214
4.1.2 THE CASE OF THE HOMOGENEOUS DIFFERENTIAL EQUATION * 216
4.1.3 THE CASE OF THE HOMOGENEOUS BOUNDARY CONDITION * 220
4.1.4 THE CASE OF A RIGHT-HAND SIDE OF ZERO AVERAGE VALUE * 222
4.1.5 CONCLUSION
-----
222
4.1.6 APPENDIX
-----
223
4.2 FORMAL ASYMPTOTIC SOLUTIONS
------
225
4.2.1 ASYMPTOTIC PHENOMENA * 225
4.2.2 BLOW-UP TECHNIQUES
-----
228
4.2.3 FORMAL ASYMPTOTIC SOLUTION * 230
4.2.4 THE EXCEPTIONAL CASE
P = 2
* 233
4.2.5 DEGENERATE PROBLEM * 235
4.2.6 GENERALIZATION TO HIGHER DIMENSIONS * 235
4.2.7 PARAMETER-DEPENDENT NORMS * 240
4.3 THE SHAPIRO-LOPATINSKII CONDITION * 241
4.3.1 BOUNDARY VALUE PROBLEMS WITH SMALL PARAMETER * 241
4.3.2 ASYMPTOTIC EXPANSION * 242
4.3.3 THE MAIN SPACES * 245
4.3.4 AUXILIARY RESULTS
-----
249
4.3.5 THE MAIN RESULT
-----
251
4.3.6 LOCAL ESTIMATES IN THE INTERIOR* 253
4.3.7 THE CASE OF BOUNDARY POINTS * 255
4.3.8 CONCLUSION
-----
257
4.4 PSEUDODIFFERENTIAL CALCULUS WITH A SMALL PARAMETER * 257
4.4.1 SINGULAR PROBLEMS WITH A SMALL PARAMETER * 257
4.4.2 LOSS OF INITIAL DATA
-----
258
4.4.3 A PASSIVE APPROACH TO OPERATOR-VALUED SYMBOLS * 260
4.4.4 OPERATORS WITH A SMALL PARAMETER * 264
4.4.5 ELLIPTICITY WITH A LARGE PARAMETER * 269
4.4.6 ANOTHER APPROACH TO PARAMETER-DEPENDENT THEORY * 269
4.4.7 REGULARIZATION OF SINGULARLY PERTURBED PROBLEMS * 275
5 ASYMPTOTIC SOLUTION OF THE SCHROEDINGER EQUATION * 278
5.1 SEMICLASSICAL APPROXIMATIONS OF QUANTUM MECHANICS * 278
5.1.1 STANDARD APPROXIMATION * 278
5.1.2 PRELIMINARY RESULTS * 280
5.1.3 THE SCHROEDINGER EQUATION FOR QUADRATIC HAMILTONIANS * 281
5.1.4 EXACT SOLUTION WITH A RAPIDLY DECREASING INITIAL SYMBOL * 282
5.1.5 SYMMETRIZED GENERATING FUNCTION * 285
5.2 ASYMPTOTIC SOLUTION OF THE SCHROEDINGER EQUATION * 286
5.2.1 SYMBOL CLASSES * 286
5.2.2 CONSTRUCTION OF A FORMAL EXPANSION * 288
5.2.3 ASYMPTOTIC SOLUTION * 289
5.2.4 ONE MORE ASYMPTOTIC DECOMPOSITION * 291
5.3 THE TRACE OF THE SCHROEDINGER OPERATOR * 292
5.3.1 ANTI-WICK SYMBOLS * 292
5.3.2 THE TRACE FORMULA * 293
5.3.3 TRACE ASYMPTOTICS FOR
H
- 0 * 293
5.3.4 A LEFSCHETZ FIXED POINT FORMULA * 294
5.4 QUANTUM DYNAMICS IN THE FERMI-PASTA-ULAM PROBLEM * 295
5.4.1 WAVE DECAY PROCESSES * 296
5.4.2 CLASSICAL LIMIT * 297
5.4.3 QUANTUM EQUATIONS OF DECAY * 299
5.4.4 ANALYSIS OF QUANTUM EQUATIONS * 302
5.4.5 EXISTENCE OF SOLUTIONS * 303
5.4.6 SUCCESSIVE APPROXIMATIONS * 307
5.4.7 ASYMPTOTIC UNDER LARGE TIME * 313
5.4.8 CONCLUSION * 314
6 THE KELVIN-HELMHOLTZ INSTABILITY * 316
6.1 DERIVATION OF THE FUNDAMENTAL EQUATION * 318
6.1.1 SETTING OF THE PROBLEM * 318
6.1.2 CONDITIONS ON THE UNKNOWN BOUNDARY * 319
6.1.3 DERIVATION OF AN EQUATION FOR THE CURVE
-----
320
6.1.4 A HAMILTONIAN FORM OF THE EQUATION OF TANGENTIAL DISCONTINUITY
-----
322
6.1.5 CONSERVATION LAWS * 323
6.2 SMALL PERTURBATION OF TANGENTIAL DISCONTINUITY * 324
6.2.1 LINEARIZATION OF THE EQUATION OF TANGENTIAL DISCONTINUITY * 324
6.2.2 ON THE ELLIPTICITY OF THE SYSTEM (6.18) * 326
6.2.3 SMALL PERTURBATIONS OF RECTILINEAR TANGENTIAL DISCONTINUITY * 327
6.2.4 THE LINEARIZATION OF EQUATION (6.17) * 328
6.2.5 REMARKS ON THE LINEARIZED SYSTEM * 329
6.3 ANALYTIC CONTINUATION FROM A BOUNDARY SUBSET * 331
6.3.1 THE RIEMANN MAPPING THEOREM * 333
6.3.2 HARDY SPACES * 334
6.3.3 THE CAUCHY FORMULA * 335
6.3.4 QUENCHING FUNCTIONS * 336
6.3.5 THE GOLUZIN-KRYLOV FORMULA * 338
6.3.6 A UNIQUENESS THEOREM * 339
6.3.7 APPROXIMATION THROUGH HOLOMORPHIC FUNCTIONS * 340
6.3.8 EXPANSION IN A FOURIER SERIES * 341
6.3.9 APPROXIMATION THROUGH LEGENDRE POLYNOMIALS * 343
6.4 A NUMERICAL APPROACH TO THE RIEMANN HYPOTHESIS * 344
6.4.1 THE RIEMANN ZETA FUNCTION * 345
6.4.2 ANALYTIC CONTINUATION IN A LUNE * 346
6.4.3 A CARLEMAN FORMULA FOR A HALF-DISK * 349
6.4.4 REDUCTION OF THE RIEMANN HYPOTHESIS * 352
6.4.5 NUMERICAL EXPERIMENTS * 355
7 NONLINEAR CAUCHY PROBLEMS FOR ELLIPTIC EQUATIONS * 357
7.1 A VARIATIONAL APPROACH TO THE CAUCHY PROBLEM * 357
7.1.1 RELAXATIONS OF ILL-POSED PROBLEMS * 357
7.1.2 THE CAUCHY PROBLEM * 359
7.1.3 VARIATIONAL SETTING * 361
7.1.4 EULER*S EQUATIONS * 364
7.1.5 EXAMPLES * 366
7.1.6 MIXED PROBLEMS * 367
7.1.7 INVERSE PROBLEM APPROACH * 369
7.2 THE CAUCHY PROBLEM FOR CHAPLYGIN*S SYSTEM * 371
7.2.1 PRELIMINARIES * 371
7.2.2 CHAPLYGIN*S SYSTEM * 372
7.2.3 VARIATIONAL SETTING* 373
7.2.4 EXISTENCE OF SOLUTIONS
-----
375
7.2.5 STABLE CAUCHY PROBLEMS * 377
7.2.6 APPROXIMATE SOLUTIONS * 379
7.3 HYPERBOLIC FORMULAS IN ELLIPTIC CAUCHY PROBLEMS * 380
7.3.1 THE CAUCHY PROBLEM * 384
7.3.2 HYPERBOLIC REDUCTION * 385
7.3.3 THE PLANAR CASE * 387
7.3.4 THE CARLEMAN FORMULA * 389
7.3.5 POISSON*S FORMULA
-----
391
7.3.6 THE KIRCHHOFF FORMULA * 393
7.3.7 CONCLUDING REMARKS * 395
7.4 A WKB SOLUTION TO THE NAVIER-STOKES EQUATIONS * 396
7.4.1 BASIC EQUATIONS OF THE DYNAMICS OF AN INCOMPRESSIBLE VISCOUS
FLUID
-----
396
7.4.2 GENERALIZED NAVIER-STOKES EQUATIONS * 398
7.4.3 ENERGY ESTIMATES
-----
401
7.4.4 FIRST STEPS TOWARDS THE SOLUTION * 403
7.4.5 A WKB SOLUTION
-----
405
BIBLIOGRAPHY * 407
INDEX
-----
421
|
| any_adam_object | 1 |
| author | Glebov, Sergej G. Kiselev, Oleg Michajlovič Tarchanov, Nikolaj Nikolaevič 1955-2020 |
| author_GND | (DE-588)1132829518 (DE-588)1132830591 (DE-588)121160521 |
| author_facet | Glebov, Sergej G. Kiselev, Oleg Michajlovič Tarchanov, Nikolaj Nikolaevič 1955-2020 |
| author_role | aut aut aut |
| author_sort | Glebov, Sergej G. |
| author_variant | s g g sg sgg o m k om omk n n t nn nnt |
| building | Verbundindex |
| bvnumber | BV045296696 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)1043869696 (DE-599)DNB1121019188 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045296696 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:14:09Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110533835 3110533839 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030683930 |
| oclc_num | 1043869696 |
| open_access_boolean | |
| owner | DE-20 |
| owner_facet | DE-20 |
| physical | XVIII, 422 Seiten Illustrationen 25 cm, 865 g |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | Nonlinear equations with small parameter / Sergey G. Glebov De Gruyter series in nonlinear analysis and applications |
| spelling | Glebov, Sergej G. Verfasser (DE-588)1132829518 aut Waves and boundary problems Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov Berlin De Gruyter [2018] XVIII, 422 Seiten Illustrationen 25 cm, 865 g txt rdacontent n rdamedia nc rdacarrier Nonlinear equations with small parameter / Sergey G. Glebov Volume 2 De Gruyter series in nonlinear analysis and applications Volume 23/2 Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Asymptotik (DE-588)4126634-1 s DE-604 Nichtlineare Gleichung (DE-588)4455337-7 s Kiselev, Oleg Michajlovič Verfasser (DE-588)1132830591 aut Tarchanov, Nikolaj Nikolaevič 1955-2020 Verfasser (DE-588)121160521 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als 9783110534986 Erscheint auch als Online-Ausgabe 9783110534979 Erscheint auch als Online-Ausgabe 9783110533903 Erscheint auch als Online-Ausgabe Waves and Boundary Problems 1. Auflage Berlin/Boston : De Gruyter, 2018 Online-Ressource, 441 Seiten Sergey G. Glebov Nonlinear equations with small parameter Volume 2 (DE-604)BV005530011 23,2 B:DE-101 application/pdf http://d-nb.info/1121019188/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030683930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Glebov, Sergej G. Kiselev, Oleg Michajlovič Tarchanov, Nikolaj Nikolaevič 1955-2020 Waves and boundary problems Nichtlineare Gleichung (DE-588)4455337-7 gnd Asymptotik (DE-588)4126634-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4455337-7 (DE-588)4126634-1 (DE-588)4128900-6 |
| title | Waves and boundary problems |
| title_auth | Waves and boundary problems |
| title_exact_search | Waves and boundary problems |
| title_full | Waves and boundary problems Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_fullStr | Waves and boundary problems Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_full_unstemmed | Waves and boundary problems Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tarkhanov |
| title_short | Waves and boundary problems |
| title_sort | waves and boundary problems |
| topic | Nichtlineare Gleichung (DE-588)4455337-7 gnd Asymptotik (DE-588)4126634-1 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Nichtlineare Gleichung Asymptotik Nichtlineare partielle Differentialgleichung |
| url | http://d-nb.info/1121019188/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030683930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT glebovsergejg wavesandboundaryproblems AT kiselevolegmichajlovic wavesandboundaryproblems AT tarchanovnikolajnikolaevic wavesandboundaryproblems AT walterdegruytergmbhcokg wavesandboundaryproblems |
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