Kevorkian J., Cole J.D. — Multiple Scale and Singular Perturbation Methods :: Электронная библиотека попечительского совета мехмата МГУ

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Kevorkian J., Cole J.D. — Multiple Scale and Singular Perturbation Methods

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Название: Multiple Scale and Singular Perturbation Methods

Авторы: Kevorkian J., Cole J.D.

Аннотация:

This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text, Perturbation Methods in Applied Mathematics (AMS 34). A new chapter dealing with regular expansions has been added, the discussion of layer-type singular perturbations has been revised, and the coverage of multiple scale and averaging methods has been significantly expanded to reflect recent advances and viewpoints. The result is a comprehensive account of the various perturbation techniques currently used in the sciences and engineering that is suitable both as graduate text and as a reference work on the subject.

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Рубрика: Математика/Анализ/Асимптотические методы, Теория возмущений/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1996

Количество страниц: 632

Добавлена в каталог: 02.04.2005

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Предметный указатель

, definition of      3
Ablowitz, M.J.      619
Ackerberg, R.C.      117
Acoustics, wave equation for      238
Acrivos, A.      250 264
Action and angle variables      446
Action and angle variables for coupled oscillators      388
Action and angle variables, normalized      448
Action for linear oscillator with slowly varying frequency      412
Action, definition of      447
Action, interval of uniform validity for      412
Adiabatic invariant for a charged particle in a slowly varying magnetic field      318
Adiabatic invariant for a model problem      438
Adiabatic invariant for a strictly nonlinear oscillator      368
Adiabatic invariant for coupled weakly nonlinear oscillators      478
Adiabatic invariant for general system in standard form      434
Adiabatic invariant for linear oscillator with slowly varying frequency      411
Adiabatic invariant for two-body problem (slowly varying mass)      465
Adiabatic invariant to $O(\epsilon)$ for linear oscillator with slowly varying frequency      414
Adiabatic invariant, definition of      413
Adiabatic invariant, global, for solutions in resonance      482
Adiabatic invariant, interval of uniform validity for      413
Airy function      240 323
Airy’s equation      79
Amplitude equation      540
Angle variable, change in after a complete cycle      448
Angle variable, definition of      447
Anisotropic elastic material, boundary conditions for      245
Anisotropic elastic material, boundary layer in      241
Anisotropic elastic material, boundary-layer expansion for      246
Anisotropic elastic material, equilibrium equations for      243
Anisotropic elastic material, outer expansion for      243
Anisotropic elastic material, stress-strain relations for      242
Argument of pericenter      326
Asymptotic expansion by repeated integrations by parts      14 18
Asymptotic expansion for a definite integral      13
Asymptotic expansion for the root of an algebraic equation      9
Asymptotic expansion of a singular integral      16
Asymptotic expansion, construction of      6
Asymptotic expansion, definition of      5
Asymptotic expansion, divergent      15
Asymptotic expansion, domain of validity for      7
Asymptotic expansion, example of nonuniform validity for      6 7
Asymptotic expansion, general, definition of      51
Asymptotic expansion, optimal number of terms for      15
Asymptotic expansion, regular      19
Asymptotic expansion, uniformly valid      5
Asymptotic expansion, uniqueness of      5
Asymptotically equivalent      305
Asymptotically equivalent expansions, definition of      10
Augmented outer expansion      78
Averaging method      280
Averaging transformation for a Hamiltonian system with a resonant pair of coordinates      482
Axisymmetric n-pole      251
Barcilon, V.      237 264
Batchelor, G.K.      261
Beam deflection      110
Beam deflection, boundary layer near right end for      114
Beam deflection, inner expansion near left end for      112
Beam deflection, matching near left end for      113
Beam deflection, matching near right end for      115
Beam deflection, outer expansion for      111
Beam deflection, uniformly valid composite expansion for      115
Beam string      110
Beating oscillations for a forced linear oscillator      356
Beating oscillations for the forced Duffing equation      312 314
Bensoussan, A.      619
Bernoulli equation      167 175 262
Biological cell (infinite cylindrical), far-field expansion for      228 231
Biological cell (infinite cylindrical), Green’s function for      227
Biological cell (infinite cylindrical), multiple-scale analysis for      237
Biological cell (infinite cylindrical), near-field expansion for      232
Biological cell (infinite cylindrical), switchback terms in near-field expansion for      234
Biot, M.      117
Bogoliubov, N.N.      280 409 410 520
Bosley, D.L.      408 520 521
Boundary layer correction      51
Boundary layer resonance      73
Boundary-layer theory in viscous incompressible flow      164
Bourland, F.J.      360 364 408 520
Boussinesq approximation for shallow water flow      570
Burgers’ equation      143
Burgers’ equation (inviscid), entropy condition for      149
Burgers’ equation (inviscid), shock condition for      149
Burgers’ equation (inviscid), weak solutions for      149
Burgers’ equation, boundary layer for      157
Burgers’ equation, boundary-value problem for      147 154 164
Burgers’ equation, centered fan for      158
Burgers’ equation, constant-speed shock layer for      150
Burgers’ equation, corner layer for      146 151 154 158
Burgers’ equation, exact solution of a homogeneous boundary-value problem for      147
Burgers’ equation, exact solution of initial-value problem for      145
Burgers’ equation, exact solutions on a finite domain for      148
Burgers’ equation, expansion of variable-speed shock layer for      153
Burgers’ equation, initial-value problem for      144
Burgers’ equation, integral equation for variable boundary condition for      148
Burgers’ equation, matching of constant-speed shock layer for      151
Burgers’ equation, matching of shock layer for      156
Burgers’ equation, matching of variable-speed shock layer for      154
Burgers’ equation, phase shift in shock layer for      156
Burgers’ equation, shock condition for variable-speed shock layer for      153
Burgers’ equation, shock layer for      146 156
Burgers’ equation, subcharacteristics for      150
Burgers’ equation, symmetry of constant-speed shock layer for      151
Burgers’ equation, transition layer for      158
Burgers’ equation, variable-speed shock layer for      152
Byrd, P.F.      408
Cable theory      237
Canonical transformation      442
Canonical transformation, generating function for      443
Canonical transformation, variational principle defining      443
Cantilever beam      241
Carrier, G.F.      35 117
Centered fan      154
Channel flow      556 600
Channel flow, conservation laws for      556
Channel flow, equations in terms of characteristic dependent variables for      558
Channel flow, evolution equation for      604
Characteristic curves, equation for      119
Charged particle in a slowly varying magnetic field      315
Charged particle in a spatially slowly varying magnetic field      457
Charged particle, adiabatic invariant for      461
Chikwendu, S.C.      619
Childress, S      264
Chirikov, B.V.      520
Classification of linear second-order partial differential equations      119
Clausius — Mossotti formula      254
Cochran, J.      408
Cole — Hopf transformation      143 147
Cole, J.D.      237 264 265 280 408 619 620
Collision solution, model problem for      108
Complete integral      446
Composite expansion      51
Conservation laws (linearized), general solution for      561
Conservation laws (linearized), necessary conditions for stability for      560
Conservation laws (linearized), stability condition for long waves for      560
Conservation laws (linearized), stability of solutions for      558
Conservation laws (periodic initial data), evolution equations for      599
Conservation laws (periodic initial data), resonance condition for      597 598
Conservation laws (weakly nonlinear, hyperbolic) for channel flow      556
Conservation laws (weakly nonlinear, hyperbolic) in terms of charcateristic dependent variables      554
Conservation laws (weakly nonlinear, hyperbolic), equations in standard form for      552
Conservation laws (weakly nonlinear, hyperbolic), shock conditions for      553
Conservation laws (weakly nonlinear, hyperbolic), source terms in      552
Conservation laws with no source terms (isolated initial data), decoupled evolution equations of Burgers’ type for      596
Conservation laws with source terms, divergence form of evolution equation for      607
Conservation laws with source terms, effect of weak dissipation for      607
Conservation laws with source terms, evolution equation for      603
Conservation laws with source terms, evolution equation with weak dissipation      608
Conservation laws with source terms, multiple-scale expansion for      601

Conservation laws with source terms, necessary condition for nonlinear stability for      606
Conservation laws with source terms, shock condition for evolution equation for      606
Contopoulos, G.      408
Cook, L.P.      619
coordinates      441
Corben, H.C.      117
Coriolis force      334 335
Corner layer      67 88 146 151 154 158
Courant, R.      264
Cumulative perturbation      21
Diffusion equation (weakly nonlinear), amplitude equation for      540
Diffusion equation (weakly nonlinear), equilibration of the linearly most unstable mode for      541
Diffusion equation (weakly nonlinear), Landau equation for      540
Diffusion equation (weakly nonlinear), model example for      551
Diffusion equation (weakly nonlinear), multiple-scale expansion for      539
Diffusion equation (weakly nonlinear), restrictions on applicability of stability, analysis for      541
Diffusion equation (weakly nonlinear), scaling corresponding to richest perturbation problem for      539
Diffusion equation (weakly nonlinear), stability analysis for      537
Dipole      250
dispersion relation      524 532
Distinguished limit, definition of      47
Drazin, P.G.      619
Duffing’s equation in standard form      388
Duffing’s equation, effect of damping on subharmonics for      357
Duffing’s equation, subharmonics for      279
d’Alembert paradox      207
Easwaran, C.V.      619
Eccentric anomaly      326
Eccentricity      326
Eckhaus, W.      541 619
Eckstein, M.C.      408
Effective conductivity, Rayleigh’s result for      250
Effective thermal conductivity      250
Eisenberg, R.S.      237 264 265
Elastic-shell theory (spherical shell)      187
Elastic-shell theory (spherical shell), boundary-layer expansion for      193
Elastic-shell theory (spherical shell), inner (membrane theory) expansion for      189
Elastic-shell theory (spherical shell), matching for      193
Elastic-shell theory (spherical shell), membrane equations for      192
Elastic-shell theory (spherical shell), membrane-theory expansion for      189
Electrical buffer      227
Electrophysiology      218
Elliptic integral      269 380
Elliptic partial differential equation      119 120
Elliptic partial differential equation as Euler’s equation for a variational principle      131
Elliptic partial differential equation in annular region      160
Elliptic partial differential equation with mixed boundary conditions      159
Elliptic partial differential equation with saddle-point singularity of subcharacteristics      161
Elliptic partial differential equation, $O(\epsilon)$ boundary layer for      122
Elliptic partial differential equation, $O(\epsilon)$ local layer for      127
Elliptic partial differential equation, $O(\epsilon^{1/2})$ boundary layer for      124
Elliptic partial differential equation, boundary layer for      121
Elliptic partial differential equation, boundary-layer equation for      123
Elliptic partial differential equation, Dirichlet problem for      120 130
Elliptic partial differential equation, discontinuous boundary data for      127
Elliptic partial differential equation, indeterminate outer limit for      129 130
Elliptic partial differential equation, initial condition for $O(\epsilon^{1/2})$ boundary layer for      126
Elliptic partial differential equation, Lagrangian for      131
Elliptic partial differential equation, location of boundary layer for      123
Elliptic partial differential equation, matching of outer and $O(\epsilon^{1/2})$ , boundary-layer limits for      125
Elliptic partial differential equation, matching of outer and boundary-layer limits for      123
Elliptic partial differential equation, mixed boundary conditions for      128
Elliptic partial differential equation, nonparallel subcharacteristics for      129
Elliptic partial differential equation, outer limit for      120
Elliptic partial differential equation, subcharacteristic boundary for      123
Elliptic partial differential equation, subcharacteristics for      121
Elliptic partial differential equation, uniqueness of solutions with mixed boundary data for      128
Elliptic partial differential equation, variational principle for      130
Elliptic sine function      381
Erdelyi, A.      35 408
Erdi, B.      408
Error function      76 146
Error function, asymptotic expansion for      15
Error function, definition of      13
Euler — Lagrange equation      74 80 81
Everstine, G.C.      264
Exponential integral      103
Extremal      74
Fermat’s principle      75
Fixed force-centers, collision orbits in      95
Fixed force-centers, energy integral for      97
Fixed force-centers, equilibrium point for      97
Fixed force-centers, inner expansion for      100
Fixed force-centers, inner variable scaling for      99
Fixed force-centers, matching of inner and outer expansions for      100
Fixed force-centers, orbits starting near the equilibrium point in      108
Fixed force-centers, outer expansion for      98
Fixed force-centers, overlap domain for      101
Flow due to a source in a uniform stream      179
Flow due to displacement thickness      173 178
Flow past a semi-infinite flat plate      181
Forced Duffing equation, multiple-scale expansion for      307
Forced motion near resonance for Duffung’s equation      307
Frenzen, C.L.      619
Fresnel integral      508
Friedman, M.D.      408
Froude number      556
Gamma function      62
Gardner, C.S.      619
Gas dynamics (isolated initial data), decoupled evolution equations of Burgers’ type for      596
Gas dynamics, Burgers’ equation for the velocity in      596
Gas dynamics, characteristics for      591
Gas dynamics, conservation laws for      588
Gas dynamics, equations in standard form for      591
Gas dynamics, equations in terms of characteristic, dependent variables for      592
Gas dynamics, multiple-scale expansion for      593
Gas dynamics, shock condition for      592
Generating function for a canonical transformation      443
Ginzburg — Landau equation      547
Global adiabatic invariants      486
Goldstein, H.      117 520
Grasman, J.      73 117 264
Greene, J.M.      619
Gregory, R.P.      264
Guiding center      458
Haberman, R.      35 360 364 408 520
Hamet, J.-F      241 264
Hamilton — Jacobi equation      444
Hamilton — Jacobi equation, time-independent      446
Hamiltonian system      441
Hamiltonian system (frequencies depend on the actions)      513
Hamiltonian system (frequencies depend on the actions), transient resononce for      513
Hamiltonian system (prescribed frequency variations), jump in the actions across resonance for      510
Hamiltonian system (prescribed frequency variations), matching of preresonance and resonance expansions for      507
Hamiltonian system (prescribed frequency variations), solution after resonance for      509
Hamiltonian system (prescribed frequency variations), solution before resonance for      503
Hamiltonian system (prescribed frequency variations), solution near resonance for      505
Hamiltonian system (prescribed frequency variations), uniformly valid expansion across resonance for      511
Hamiltonian system (resonant pair of coordinates), averaging transformation for      482
Hamiltonian system (resonant pair of coordinates), global adiabatic invariants for      486
Hamiltonian system (resonant pair of coordinates), isolating transformation for      482
Hamiltonian system with a resonant pair of coordinates      482
Hamiltonian systems in standard form, adiabatic invariants for      470
Hamiltonian systems in standard form, examples of      471
Hamiltonian systems in standard form, near-identity averaging transformations for      440 466
Hamiltonian, general periodic in one degree of freedom      452
Hamiltonian, separable      446
Hamilton’s modified principle      442
Hamilton’s principle      75
Heat conduction (steady one-dimensional) with slowly and rapidly varying thermal conductivity      614
Heat conduction (steady one-dimensional), effective thermal conductivity for      617
Heat conduction (steady one-dimensional), equation for      614
Heat conduction (steady one-dimensional), heat flux for      617
Heat conduction (steady one-dimensional), homogenized equation for      617
Heat conduction (steady one-dimensional), multiple-scale expansion for      614
Heat conduction (steady two-dimensional), conservation equation for      617
Heat conduction (steady two-dimensional), heat flux components for      619
Heat conduction (steady two-dimensional), homogenized conservation equation for      618
Heat conduction (steady two-dimensional), multiple-scale expansion for      617
Heat conduction (steady)      159

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