Holdings: Waves and boundary problems

Waves and boundary problems:

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Bibliographic Details
Main Authors:	Glebov, Sergej G. (Author), Kiselev, Oleg Michajlovič (Author), Tarchanov, Nikolaj Nikolaevič 1955-2020 (Author)
Format:	Book
Language:	English
Published:	Berlin De Gruyter [2018]
Series:	Nonlinear equations with small parameter / Sergey G. Glebov Volume 2 De Gruyter series in nonlinear analysis and applications Volume 23/2
Subjects:	Nichtlineare Gleichung Asymptotik Nichtlineare partielle Differentialgleichung
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XVIII, 422 Seiten Illustrationen 25 cm, 865 g
ISBN:	9783110533835 3110533839

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MARC


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Record in the Search Index

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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 EULERS 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 CHAPLYGINS SYSTEM 371 7.2.1 PRELIMINARIES * 371 7.2.2 CHAPLYGINS 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 POISSONS 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
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ctrlnum	(OCoLC)1043869696 (DE-599)DNB1121019188
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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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