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| Авторизация |
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| Kevorkian J., Cole J.D. — Multiple Scale and Singular Perturbation Methods |
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| Предметный указатель |
Heat conduction (steady) in a cylindrical rod 261
Heat conduction (steady) in a long rod 183
Heat conduction (steady) with axial symmetry 163
Heat conduction (steady), boundary-layer expansion for 185
Heat conduction (steady), matching condition for 186
Heat conduction (steady), outer expansion for 184
Heat conductivity for a sphere in an infinite medium 251
Heat conductivity for an array of spheres in an infinite medium 252
Heat-flow problem, nonlinear cylindrically symmetric 102
Hilbert, D. 264
Hill, G.W. 335
Hill’s equations 335
Homogenization, limit process expansions for 249
Homogenization, using multiple-scale expansions 614
Hooke’s law 110
Hoop stress 188
Hopf, E. 264
Hori, G.I. 408
Howard, L.N. 265
Hyperbolic conservation laws with source terms 552
Hyperbolic partial differential equation 119 132
Hyperbolic partial differential equation, boundary-layer expansion for, incoming subcharacteristics 143
Hyperbolic partial differential equation, characteristics for 133
Hyperbolic partial differential equation, distinguished inner limit for (outgoing subcharacteristics) 141
Hyperbolic partial differential equation, incoming subcharacteristics for 142
Hyperbolic partial differential equation, initial-value problem for 134
Hyperbolic partial differential equation, initially valid expansion for 136
Hyperbolic partial differential equation, inner expansion for (outgoing subcharacteristics) 141
Hyperbolic partial differential equation, matching of initially valid and outer expansions for 138
Hyperbolic partial differential equation, matching of outer and interior-layer expansion for (outgoing subcharacteristics) 142
Hyperbolic partial differential equation, outer expansion for 138
Hyperbolic partial differential equation, outer limit for 135
Hyperbolic partial differential equation, outer limit for (incoming subcharacteristics) 142
Hyperbolic partial differential equation, outer limit for (outgoing subcharacteristics) 140
Hyperbolic partial differential equation, outgoing subcharacteristics for 140
Hyperbolic partial differential equation, propagation of jumps in derivatives for 135
Hyperbolic partial differential equation, role of the small parameter in 132
Hyperbolic partial differential equation, signaling problem for 139
Hyperbolic partial differential equation, stability conditions for 135
Hyperbolic partial differential equation, validity in the far field for 133 139
Indeterminacy of outer limit 73
Indeterminacy of outer limit, a variational principle for resolving 74
Indeterminacy of outer limit, augmented outer expansion to resolve 77
Indeterminacy of outer limit, symmetry argument for resolving 73
Inner expansion, definition of 7
Integral conservation law 149
Integral conservation law, general scalar 149
Internal-layer 511
Isentropic 591
Isolating transformation for a Hamiltonian system with a resonant pair of coordinates 482
Isothermal shock 94
Jacobi integral 334 359
Kabakow, H. 408
Kaplun, S. 172 212 215 264
Kath, W.L. 520
Keller, J.B. 619 620
Keplerian elements 331
Keplerian, ellipse 96
Keplerian, hyperbola 96
Keplerian, orbit 95
Kepler’s equation 326 330
Kevorkian, J. 35 117 264 408 409 520 521 619 620
Kogelman, S. 620
Korteweg-de Vries equation 274
Korteweg-de Vries equation (linearized) 275
Korteweg-de Vries equation (linearized), dispersion relation for 276
Korteweg-de Vries equation (linearized), traveling wave solution for 275
Korteweg-de Vries equation (weakly nonlinear), multiple-scale expansion for 549
Korteweg-de Vries equation (weakly nonlinear), strained coordinate expansion for 276
Korteweg-de Vries equation (weakly nonlinear), traveling wave solution for 276
Korteweg-de Vries equation, forced 584
Korteweg-de Vries equation, nonexistence of outer limit for 576
Krook, M 35 117
Kruskal, M.D. 619
Krylov, N.M. 280 409 410 520
Kuo, Y.H. 268
Kuzmak, G.N. 280 359 360 363 409 429
Kuzmak’s method 280
Lagerstrom, P.A. 73 101 117 212 264 265
Lagrange equations 442
Lagrangian 74 75 80 81 442
Lagrangian, nonuniqueness for a given differential equation 74 80
Lamb, H. 265
Lancaster, J.E. 117
Landau equation 540
Landau, L. 261 265
Landauer, R. 249 265
Lange, C.G. 78 117
Laplace, P.-S. 324 409
Lardner, R.W. 620
Least degeneracy, principle of 11
Legendre transformation 442
Lewin, L. 520
Li, H.K. 520
Li, Y.R 409 520
Libai, A. 265
Lichtenberg, A.J. 521
Lick, W. 409
Lie transforms 471
Lieberman, M.A. 521
Lifschitz, E. 261 265
Lighthill, M.J. 265 268 274
Limit cycle 272
Limit process expansion for partial differential equations 118
Limit process expansion, definition of 47 49
Lindstedt, A. 268
Linear oscillator (small damping) 37 280
Linear oscillator (small damping), exact solution for 281
Linear oscillator (small damping), frequency shift for 287
Linear oscillator (small damping), nonexistence of limit process expansion over long time for 282
Linear oscillator (small damping), regular expansion for 38 53
Linear oscillator (small damping), two-scale expansion as a general asymptotic expansion for 283
Linear oscillator (small damping), two-scale expansion for 282
Linear oscillator (small damping), two-scale expansion from differential equation for 285
Linear oscillator (small damping), uniformly valid result for 287
Linear oscillator (small mass) 38
Linear oscillator (small mass), direct matching condition to  for 46
Linear oscillator (small mass), direct matching condition to O(1) for 46
Linear oscillator (small mass), exact solution for 40
Linear oscillator (small mass), extended domain of validity of inner limit for 43
Linear oscillator (small mass), extended domain of validity of outer limit for 42
Linear oscillator (small mass), extended domain of validity of two-term inner expansion for 45
Linear oscillator (small mass), extended domains of validity for 41
Linear oscillator (small mass), inner expansion for 41 48
Linear oscillator (small mass), inner limiting equation for 47
Linear oscillator (small mass), intermediate limit for 47
Linear oscillator (small mass), limit process expansions for 48
Linear oscillator (small mass), matching for 50
Linear oscillator (small mass), modified outer expansion for 52
Linear oscillator (small mass), outer expansion for 41 48
Linear oscillator (small mass), outer limiting equation for 47
Linear oscillator (small mass), overlap of extended domains of validity for 45
Linear oscillator (small mass), uniformly valid composite expansion for 51
Linear oscillator with slowly varying frequency 315 368 411 449
Linear singular perturbation problem, boundary-layer limit for 55
Linear singular perturbation problem, example with an interior layer for 66
Linear singular perturbation problem, example with analytic coefficients for 58
Linear singular perturbation problem, example with corner layer for 67
Linear singular perturbation problem, example with nonanalytic coefficients for 60
Linear singular perturbation problem, example with two boundary layers for 67
Linear singular perturbation problem, existence of solutions for 54
Linear singular perturbation problem, inner expansion for 56
Linear singular perturbation problem, matching to 0(1) for 57
Linear singular perturbation problem, outer expansion for 55
Linear singular perturbation problem, sufficient conditions for existence of simple boundary layers for 55
Linear singular perturbation problem, uniformly valid approximation to 0(1) for 58
Lions, J.-L. 619
Liu, C.-S. 265
Love, A.E.H. 265
Low Reynolds number flow past a circular cylinder 212
| Low Reynolds number flow past a circular cylinder, inner (Stokes) expansion for 213
Low Reynolds number flow past a circular cylinder, matching of inner and outer expansions for 217
Low Reynolds number flow past a circular cylinder, matching of Stokes expansion at infinity for 215
Ludwig, D. 265
Luke, J.C. 360 363 364 409 429 620
MacGillivray, A.D. 77
Mahoney, J.J. 409
Majda, A. 620
Matching condition for a boundary-value problem 23
Mathieu’s equation 439
Mathieu’s equation, periodic solutions for 279
Matkowsky, B.J. 73 117 264 537 620
Maxwell equation 316
Mean anomaly 464
Method of averaging 410
Mitropolski, Y.A. 521
Miura, R.M. 619
Mixed-secular term, definition of 268
Modulus of elasticity 189
Momenta 441
Morrison, J.A. 297 409 521
Multiple-scale expansions for systems in standard form 386 395
Multiple-scale expansions, comparison with near-identity averaging transformations of 431
Multiple-scale expansions, original references to 280
Murray, J.D. 35
Navier — Stokes equations 166 213 216
Navier — Stokes equations for a weak shock layer 143
Navier — Stokes equations for viscous incompressible flow past a body 173
Near-identity averaging transformations for a general system in standard form 421
Near-identity averaging transformations for a model problem in one degree of freedom 414
Near-identity averaging transformations for Hamiltonian systems in standard form 440 466
Near-identity averaging transformations to remove oscillatory terms to 424
Near-identity averaging transformations to remove oscillatory terms to  425
Near-identity averaging transformations, averaged equations derived by 427
Near-identity averaging transformations, comparison with multiple-scale expansions of 431
Near-identity averaging transformations, role of arbitrary terms in 427
Near-identity averaging transformations, summary of results for 431
Near-identity transformation 410 413 421
Neu.J.C 521
No-slip condition 166
Nonlinear model singular perturbation problem 82
Nonlinear model singular perturbation problem, layer for 83
Nonlinear model singular perturbation problem,  layers for 85
Nonlinear model singular perturbation problem, comer layer for 88
Nonlinear model singular perturbation problem, limit with algebraic decay for 90
Nonlinear model singular perturbation problem, matching of transition and inner layers for 93
Nonlinear model singular perturbation problem, outer limit for 82
Nonlinear model singular perturbation problem, shock layer for 86
Nonlinear model singular perturbation problem, transition layer for 90
o, definition of 3
Ohm’s Law 219
Order symbols 1
Oscillator (general, weakly nonlinear) in standard form 404
Oscillator (general, weakly nonlinear), transformation to standard form for 455
Oscillator (small cubic damping), two-scale expansion for 287
Oscillator (small cubic nonlinearity) 268
Oscillator (small cubic nonlinearity), energy integral for 269
Oscillator (small cubic nonlinearity), exact solution for 270
Oscillator (small cubic nonlinearity), period for 269
Oscillator (small cubic nonlinearity), strained coordinate expansion for 271
Oscillator (small quadratic nonlinearity), strained coordinate expansion for 278
Oscillator (strictly nonlinear) 454
Oscillator (strictly nonlinear), adiabatic invariant for 368
Oscillator (strictly nonlinear), average action to 0(1) for 367
Oscillator (strictly nonlinear), condition on the fast scale for 363
Oscillator (strictly nonlinear), dependence on initial conditions for 373
Oscillator (strictly nonlinear), dissipation for 367
Oscillator (strictly nonlinear), escape from a potential well for 382
Oscillator (strictly nonlinear), escape time for 383
Oscillator (strictly nonlinear), example with cubic nonlinearity 378
Oscillator (strictly nonlinear), Fourier series expansion for 385
Oscillator (strictly nonlinear), frequency shift for 370
Oscillator (strictly nonlinear), Hamiltonian for 454
Oscillator (strictly nonlinear), Kuzmak’s method for 359
Oscillator (strictly nonlinear), periodicity conditions for 363
Oscillator (strictly nonlinear), synchronized initial conditions for 378
Oscillator (strictly nonlinear), transformation to standard form for 454
Oscillator (strictly nonlinear), two-scale expansion for 359
Oscillator (weakly nonlinear) with slowly varying frequency 478
Oscillator (weakly nonlinear, autonomous) 280
Oscillator (weakly nonlinear, autonomous) with f depending on  293
Oscillator (weakly nonlinear, autonomous) with negative damping and soft spring 291
Oscillator (weakly nonlinear, autonomous), scaling for 291
Oscillator (weakly nonlinear, autonomous), solution of, using near-identity averaging transformations 439
Oscillator (weakly nonlinear, autonomous), two-scale expansion for general 295
Oscillators (coupled, linear), frequency shift for 343
Oscillators (coupled, linear), multiple-scale expansion for 338
Oscillators (coupled, weakly nonlinear) in standard form 405
Oscillators (coupled, weakly nonlinear) with slowly varying frequencies 478
Oscillators (coupled, weakly nonlinear), adiabatic invariants for 478
Oscillators (coupled, weakly nonlinear), first resonance condition for 348
Oscillators (coupled, weakly nonlinear), multiple-scale expansion for 343
Oscillators (coupled, weakly nonlinear), necessary conditions for bounded solutions for 344
Oscillators (coupled, weakly nonlinear), periodic energy exchange in 354
Oscillators (coupled, weakly nonlinear), periodic solution for 355
Oscillators (coupled, weakly nonlinear), second resonance condition for 350
Oscillators (coupled, weakly nonlinear), solution near first resonance for 350
Oscillators (coupled, weakly nonlinear), transformation to standard form for 456
Oscillators (coupled, with slowly varying frequencies), global adiabatic invariant for 489
Oseen equations 216
Oseen flow 212
Outer expansion, definition of 7
Overlap domain, definition of 45
O’Brien, R. 261 265
O’Malley, R.E., Jr. 117
Papanicolaou, G. 619
Parabolic partial differential equation 119
Passage through resonance 411
Pearson, C.E. 35 117
Pearson, J.R.A. 265
Pechuzal, G. 620
Peierls, R. 261 265
Pendulum with slowly varying length 385
Perturbed eigenvalue problem 529
Peskoff, A. 265
Pipkin, A.C. 241 264 265
PLK method 268
Poincare, H. 268 409
Point source of current in a biological cell 218
Point source of current in a biological cell, boundary conditions for 220
Point source of current in a biological cell, initially valid expansion for 222
Point source of current in a biological cell, matching of initially valid and long time expansions for 225
Point source of current in a biological cell, outer (long time) expansion for 220
Poisson ratio 189 242
Prandtl number 588
Prandtl, L. 165 265
Proudman, I. 265
Quadrupole 250
Radial viscous inflow 168
Radial viscous inflow, inner expansion for 169
Radial viscous inflow, mass-flow defect in 172
Radial viscous inflow, matching of pressures for 170
Radial viscous inflow, matching of velocities for 170
Radial viscous inflow, Navier — Stokes equations for 169
Radial viscous inflow, outer expansion for 169
Radial viscous inflow, uniformly valid composite expansion for 172
Rayleigh, Lord 238 241 250 253 256 257 260 265 343 409
Rayleigh’s equation 272
Rayleigh’s equation, approach to limit cycle for 290
Rayleigh’s equation, limit cycle for 272
Rayleigh’s equation, strained coordinate expansion for 273
Rayleigh’s equation, two-scale expansion for 289
Rayleigh’s summability 257 260 261
Regular expansion for a boundary-perturbation problem 30
Regular expansion for a first-order equation 20
Regular expansion for a perturbed eigenvalue problem 24
Regular expansion for a perturbed oscillator 21
Regular expansion for a perturbed two-point boundary-value problem 22 34
Regular expansion for a weakly nonlinear eigenvalue problem 34
Regular expansion for weakly nonlinear vibrating string 34
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