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

Regular expansion, necessary condition for      33
Regular perturbation problem      24
Reid, W.H.      619
Resonance amplification in Duffing’s equation      310
Resonance for a general system in standard form      403
Resonance in coupled weakly nonlinear oscillators      348
Resonance, involving three or more coordinates      495
Resonance, model equation for      357
Resonance, model problem for      406
Resonance, transient      502
Resonances, simultaneous      497
Resonant pair of coordinates for a general system in standard form      489
Resonant pair of coordinates in a Hamiltonian system      482
Restricted three-body problem      96 332
Restricted three-body problem, close lunar satellite motion in      332
Reynolds number      588
Richest limit, definition of      11
Roll wave      607
Rosales, R.      620
Sandri, G.      409
Sangani, A.S.      250 264
Satellite motion (slowly varying mass), adiabatic invariants to $O(\epsilon)$ for      478
Satellite motion in standard form      388
Satellite motion with small drag using near-identity averaging transformations      439
Satellite motion, decay of orbit due to drag in      328
Satellite motion, general equations for      325
Satellite motion, including lift      358
Satellite motion, two-scale expansions for      324
Satellite motion, unperturbed orbit in      325
Segur.H.      619
Shallow water flow $(F\approx 1)$ , forced Korteweg-de Vries equation for      584
Shallow water flow $(F\approx 1)$ , isolated bottom disturbance for      581
Shallow water flow $(F\approx 1)$ , scaling for richest equations for      583
Shallow water flow $(F\neq 1)$ with an isolated bottom disturbance      577
Shallow water flow $(F\neq 1)$ , multiple-scale expansion for      578
Shallow water flow $(F\neq 1)$ , shock conditions for      581
Shallow water flow $(F\neq 1)$ , solution to leading order for      579
Shallow water flow (signaling problem), evolution equations for      585
Shallow water flow (signaling problem), multiple-scale expansion for      585
Shallow water flow (signaling problem), shock condition for evolution equation for      586
Shallow water flow, Boussinesq approximation for      570
Shallow water flow, conservation laws for      569
Shallow water flow, decoupled evolution equations for      572
Shallow water flow, down an inclined open channel      556
Shallow water flow, isolated disturbance over a flat bottom for      573
Shallow water flow, Korteweg-de Vries equation for      572 573
Shallow water flow, multiple-scale expansion for      571
Shallow water flow, over an isolated bump      570
Shallow water flow, shock condition for      569 574
Shallow water flow, shock condition for evolution equation for      574
Shallow water flow, shock trajectory for      575
Shallow water flow, surface disturbances over a flat bottom for      570
Shallow water waves      274
Shi, Y.Y.      408
Shock condition for a general scalar integral conservation law      150
Shock-layer      86 146 156 511
Similarity solution of boundary-layer equations      180
Simmonds, J.G.      265
Singular boundary problems      95
Singular boundary problems for partial differentia] equations      182
Singular perturbation problem      23
Skin friction      179 180
Slender body in a uniform stream, boundary conditions for      199
Slender body in a uniform stream, force on      201 206
Slender body in a uniform stream, force on the nose for      210
Slender body in a uniform stream, inner expansion for      204
Slender body in a uniform stream, inner expansion near the nose for      210
Slender body in a uniform stream, matching for      204 205
Slender body in a uniform stream, matching near the nose for      211
Slender body in a uniform stream, nonuniformity near the nose for      209
Slender body in a uniform stream, outer expansion for      202
Slender body in a uniform stream, radially deforming      198
Slender body in a uniform stream, switchback term in inner expansion for      205
Slender body of revolution (radially deforming), self-induced motion for      262
Sound wave, incident on a sphere      261
Source      250
Spacelike arc      133
Srinivasan, R.      117 620
Stagnation-point flow      179
Standard form for a model problem in one degree of freedom      390
Standard form for a system of first-order differential equations      386 410
Standard form for Duffing’s equation      388
Stehle, R      117
Stokes equations      213
Stokes flow      212
Stokes variables      212
Stokes — Oseen model problem      101
Stokes — Oseen model problem, inner expansion for      104
Stokes — Oseen model problem, matching for      104
Stokes — Oseen model problem, outer expansion for      102
Stokes — Oseen model problem, proof of validity of outer limit for      107
Stokes — Oseen model problem, switchback term in      105
Stokes, G.G.      268 275 409
Strained coordinate expansion, applicability of      274
Strained coordinate expansion, interval of uniform validity for      272 280

Strained coordinate expansion, method of      268
Strictly hyperbolic      552
Struble, R.A.      409
Sturm — Liouville equation, expansion near the turning point for      322
Sturm — Liouville equation, matching of transition and two-scale expansions for      323
Sturm — Liouville equation, solution near a turning point for      319
Sturm — Liouville equation, two-scale expansion for      321
Subcharacteristics      121
Supersonic thin airfoil theory, equation for velocity potential for      612
Supersonic thin airfoil theory, evolution equations for      613
Supersonic thin airfoil theory, multiple-scale expansion for      613
Supersonic thin airfoil theory, strained characteristic coordinates for      613
Suspension bridge, deflection for      116
Sustained resonance      411
Szebehely, V.      117
Taylor, R.D.      265
Theodorsen, T.      261 265
Timelike arc      133
Timoshenko, S.      266
Transcendentally small term      4
Transient resonance for Hamiltonian systems with prescribed frequency variations      502
Transition layer      90—94 158
Two-body problem (slowly varying mass)      461
Two-body problem (slowly varying mass), adiabatic invariants for      465
Two-body problem (slowly varying mass), Hamiltonian for      462
Two-body problem (slowly varying mass), Hamiltonian in standard form for      465
Two-body problem (slowly varying mass), transformation to standard form for      463
Two-scale expansion for a model problem in one degree of freedom in standard form      390
Two-scale expansion, applicability to bounday-layer, problems of      304
Uniform validity of multiple-scale expansions for a general system in standard form      404
Uniformity of O      1
van der Pol equation      272
Van Dyke, M      268 409
Variational Principle      442
Variational principle for a differential equation with a turning point      74
Viscous incompressible flow, inner expansion for      167 176
Viscous incompressible flow, matching of pressures for      177
Viscous incompressible flow, matching of velocities for      178
Viscous incompressible flow, Navier — Stokes equations in terms of potential lines and streamlines for      173
Viscous incompressible flow, optimal coordinates in      172
Viscous incompressible flow, outer expansion for      166 176
Viscous incompressible flow, vorticity propagation in      166
Viscous stress      174
Volosov, V.M.      521
von Karman, T.      117
von Zeipel, H.      411 471 521
Wan, F.Y.M.      264 266
Wang, L.      521 620
Water waves      268
Wave equation (cubic damping)      565 612
Wave equation (cubic damping), nonperiodic initial conditions for      609
Wave equation (cubic damping), waves in both directons for      566
Wave equation (cubic damping), waves in one direction for      564
Wave equation (strictly nonlinear, dispersive), slowly varying traveling waves for      535
Wave equation (weakly nonlinear) in a slowly varying domain      478
Wave equation (weakly nonlinear), traveling wave solution for      278
Wave equation (weakly nonlinear, dispersive) with convolution nonlinearity      550
Wave equation (weakly nonlinear, dispersive), boundary-value problem for      528
Wave equation (weakly nonlinear, dispersive), limitations of multiple-scale expansions for slowly varying traveling waves for      534
Wave equation (weakly nonlinear, dispersive), multiple-scale expansion for slowly varying traveling waves for      531
Wave equation (weakly nonlinear, dispersive), periodic traveling waves for      524
Wave equation (weakly nonlinear, dispersive), solution of, by Fourier transforms      527
Wave equation (weakly nonlinear, dispersive), three discrete initial waves for      549
Wave equation (weakly nonlinear, dispersive), two discrete initial waves for      548
Wave equation (weakly nonlinear, dispersive), two-scale expansion for      525
Wave equation (weakly nonlinear, nondispersive) in terms of characteristic dependent variables      562
Wave equation (weakly nonlinear, nondispersive), evolution equations obtained by removing inconsistent terms in      564
Wave equation (weakly nonlinear, nondispersive), multiple-scale expansion for      562
Wave equation (weakly nonlinear, nondispersive), saw-tooth wave for      610
Wave equation, exact solution for      161
Wave equation, nonlinear      522
Wave equation, signal for large time for      163
Wave equation, signaling problem for      162
Wave equation, stability condition for      162
Wave equation, weakly nonlinear, dispersive      524
Wave equation, weakly nonlinear, nondispersive      524
Weakly nonlinear stability (Eckhaus model), amplitude equation for      545
Weakly nonlinear stability (Eckhaus model), general initial conditions for      546
Weakly nonlinear stability (Eckhaus model), Ginzburg — Landau equation for      547
Weakly nonlinear stability (Eckhaus model), multiple-scale expansion for      544
Weakly nonlinear stability (Eckhaus model), scaling for      544
Weakly nonlinear stability (Eckhaus model), steady-state solution for      545
Weakly nonlinear stability, Eckhaus model for      542
Weakly nonlinear stability, Matkowsky’s model for      537
Weinitschke, H.J.      266
Weyl.H.      180 266
Whispering gallery modes      238
Whispering gallery modes, boundary condition for      238
Whispering gallery modes, boundary-layer coordinate for      239
Whispering gallery modes, modal dispersion relation for      239
Whitham, G.B.      266 409 620
Whittaker, E.T.      409
Woinowsky-Krieger, S.      266
Yu, J.      620
Zero divisors      482

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