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| Ïîèñê ïî óêàçàòåëÿì |
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| Rogers C., Ames W.F. — Nonlinear boundary value problems in science and engineering |
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| Ïðåäìåòíûé óêàçàòåëü |
Acceleration, potential, Truesdell’s 161
Algebra, Lie, 238—240
Algebra, Lie, anti-commutativity 239
Algebra, Lie, bilinearity 238
Algebra, Lie, commutator (Lie bracket) 238
Algebra, Lie, commutator table 239 240
Algebra, Lie, glossary of terms 390—392
Algebra, Lie, Jacobi identity 239
Atmospheric frontogenesis 76—88
Backlund transformation 2 3 14
Backlund transformation with reciprocal transformation 33—37
Backlund transformation, Loewner-type 169 170
Backlund transformation, reciprocal 107
Backlund transformation, strong 151
Backlund transformation, weak 150 152
Bergman expansion 92 98 124—145
Bergman expansion, Pade extension 134—145
Bergman expansion, termination 179—189
Bergman integral operator method 180
Boundaries, invariant 241
Boundaries, invariant, heat equation 241—246
Boundaries, invariant, Stefan-type, moving 241—246
Boundary conditions, insulated 28
Boundary conditions, invariance of 217
Boundary conditions, moving-type 108
Boundary conditions, nonlinear 91
Boundary conditions, Robin-type 131
Boundary conditions, Stefan — Boltzmann type 133
Boundary value problems, nonlinear, Burgers’ hierarchy 5—11
Boundary value problems, nonlinear, conservation law 16
Boundary value problems, nonlinear, coupled reciprocal and Backlund transformation 33—37
Boundary value problems, nonlinear, cylindrical 134 135
Boundary value problems, nonlinear, invariance of 215
Boundary value problems, nonlinear, moving 117
Boundary value problems, nonlinear, reciprocal transformation 16 20 35 109
Boundary value problems, nonlinear, reduction to linear 9—11
Boundary value problems, nonlinear, spherical 134 135
Boundary value problems, nonlinear, Stefan — Boltzmann 134—135
Boussinesq, equation 278
Boussinesq, fluid 82
Burgers, equation 45
Burgers, hierarchy 9 36
Canonical coordinates, group analysis 320—322
Canonical coordinates, Riemann — Volterra 14
Cauchy — Riemann equations 203
Commutator 7
Computer algebra packages, applications to group analysis 213
Conditions, Faa de Bruno 120
Conservation principle 16
Conservation principle, Ertel-type 84
Cooling, Newton’s law 132
Dilation (dilation or scaling) group 247 248
Dilation (dilation or scaling) group, invariants 249
Duality principle, Adkins’ 205
Elastic materials, deformation, finite plane strain 189—204
Elastic materials, deformation, homogeneous strain 197 198
Elastic materials, deformation, twisting of circular hole 198 199
Elasticity, nonlinear, group analysis 263—270
Elasticity, nonlinear, group generators 265
Equations, Boussinesq 278
Equations, Burgers 5
Equations, Cauchy — Riemann 203
Equations, Ermakov 150—155
Equations, evolution 19
Equations, heat conduction 5 239
Equations, hydrodynamic 61
Equations, Kadomtsev — Petviashvili 276
Equations, Kadomtsev — Petviashvili, potential 279
Equations, Korteweg — de Vries, linear 10
Equations, Korteweg — de Vries, nonlinear 278
Equations, Liouville 2 3 185
Equations, Monge — Ampere 4
Equations, Pinney 154
Equations, Riccati 174
Equations, Stokes — Beltrami 65
Equilibrium equations, Lagrangian 200
Ermakov invariant 152
Ertel potential vorticity 84
Exact shooting, boundary value problems 325—330
Exact shooting, eigenvalue problems 330—340
Exact shooting, examples 328—330 333—340
Exact shooting, second-order differential equations 327
Exact shooting, third-order differential equations 328
Exact shooting, transformation of eigenvalues to boundary conditions 330 332 336 337
Expansion, Bergman type 92—98
Expansion, Tao type 94—104
Faa de Bruno’s relation 100 120
Falkner — Skan flow 250
Flow, two-phase 37—48
Fokker — Planck equation see “Equation”
Forsyth — Hopf — Cole transformation 6—9 13 46
Frontogenesis equation, reduced to linear 86
Gas law, Karman — Tsien-type 147
Gas law, Prim-type 77 78
Geo potential 79
Group analysis, Lie invariance, boundary layer 246—251
Group analysis, Lie invariance, calculation near singularity 340—342
Group analysis, Lie invariance, canonical variables 320—322
Group analysis, Lie invariance, construction of 213—226
Group analysis, Lie invariance, determining equations 220—223
Group analysis, Lie invariance, Euler equations 309
Group analysis, Lie invariance, finite differences 342—344
Group analysis, Lie invariance, generator and extensions 220—223
Group analysis, Lie invariance, infinitesimal transformations 216
Group analysis, Lie invariance, invariant solution 224
Group analysis, Lie invariance, Kadomtsev — Petviashvili 276—279
Group analysis, Lie invariance, Korteweg — de Vries 275 276
Group analysis, Lie invariance, Navier — Stokes 308—311
Group analysis, Lie invariance, nonlinear elasticity 263—270
Group analysis, Lie invariance, ordinary differential equation, second-order 314—323
Group analysis, Lie invariance, partial differential equation, second-order 215—226
Group analysis, Lie invariance, potential Kadomtsev — Petviashvili 279
Group analysis, Lie invariance, potential modified Kadomtsev — Petviashvili 284 285
Group analysis, Lie invariance, reacting flows 251—263
Group analysis, Lie invariance, reduction in order 226
Group analysis, Lie invariance, similarity variables 224
Group analysis, Lie invariance, surface condition 224
Group analysis, Lie invariance, symmetry reduction 223 226
Group analysis, Lie invariance, von Karman 271—274 (see also “Group generators”)
Group generators, for equations, axially symmetric wave 362
Group generators, for equations, baroclinic layer 376
Group generators, for equations, Blasius 318—323
Group generators, for equations, boundary layer, power law 246—251
Group generators, for equations, boundary layer, steady on arbitrary surfaces 370
Group generators, for equations, boundary layer, three-dimensional incompressible 368 369
Group generators, for equations, boundary layer, two-dimensional incompressible 370 371
Group generators, for equations, boundary layer, two-dimensional prescribed pressure 371—373
Group generators, for equations, boundary layer, two-dimensional with moment stresses 373
Group generators, for equations, Boussinesq-type 354 355
Group generators, for equations, Burgers’ potential 348 349
Group generators, for equations, Davey — Stewartson 364 365
Group generators, for equations, diffusion, nonlinear 347 348
Group generators, for equations, elastic string, nonlinear 383
Group generators, for equations, elasticity, nonlinear 263—270
Group generators, for equations, Euler 309
Group generators, for equations, heat convection, steady 378
Group generators, for equations, Helmholtz, cylindrical 361 362
Group generators, for equations, Hopf 349—351
Group generators, for equations, Jimbo — Miwa 358
Group generators, for equations, Kadomtsev — Petviashvili 276—279
Group generators, for equations, Kadomtsev — Petviashvili, generalized cylindrical 357 358
Group generators, for equations, Kadomtsev — Petviashvili, potential 279
Group generators, for equations, Kadomtsev — Petviashvili, potential modified 284 285
Group generators, for equations, Korteweg — de Vries 275 276
Group generators, for equations, Korteweg — de Vries — Burgers 355 356
Group generators, for equations, Laplace 359 360
Group generators, for equations, Liouville 360 361
Group generators, for equations, long pipe flow 376 377
Group generators, for equations, magnetohydrodynamic, steady 381
Group generators, for equations, magnetohydrodynamic, transient 380
| Group generators, for equations, Maxwell 385 386
Group generators, for equations, moving threadline 383 384
Group generators, for equations, Navier — Stokes 308—311
Group generators, for equations, neo-Hookean material 384 385
Group generators, for equations, ordinary differential equation, second-order 317 318
Group generators, for equations, plasma, one-dimensional 378 379
Group generators, for equations, plasma, two-component 379 380
Group generators, for equations, polytropic gas 365 366
Group generators, for equations, potential flow 367 368
Group generators, for equations, reacting flow 251—263
Group generators, for equations, relativistic pencil 381 382
Group generators, for equations, Schrodinger, cubic 353 354
Group generators, for equations, Schrodinger, nonlinear 363 364
Group generators, for equations, transonic 374 375
Group generators, for equations, transonic, Lin — Tsien 373 374
Group generators, for equations, transonic, steady 375 376
Group generators, for equations, von Karman 271—274
Group generators, for equations, wave 351
Group generators, for equations, wave, semi-linear 352 353
Group, dilation 248
Group, invariants 249
Group, one parameter 214 215
Group, properties 214 215
Group, rotation 312
Hard materials 175
Heat conduction, nonlinear, generators 342
Heat conduction, nonlinear, inhomogeneous half space 123—133
Heat conduction, nonlinear, invariant finite differences 342—344
Heat conduction, nonlinear, similarity solution 92
Heat conduction, nonlinear, simple metals 20—30
Heat conduction, nonlinear, single phase moving boundary 106—111
Heat conduction, nonlinear, solid hydrogen 30—33
Heat conduction, nonlinear, two-phase Stefan problem 111—117
Hodograph 170 172 179
Hydrodynamic equations 61
Hydrogen, solid heat conduction 30—33
Hydrostatic approximation 79
Hyperbolic equation 50
Hyperbolic equation, reciprocal transformation 50
Hyperelastic material 154—157
Hyperelastic material, stress tensor 156
Inequality, Rivlin — Saunders 163
Infiltration, with prescribed flux 11—14
Initial value problem, Cauchy 179—189
Interface condition 101 102 119
Interface condition in two-phase conduction 115
Invariance of numerical algorithms of truncation error 343
Invariance of numerical algorithms under scaling 343
Invariance of numerical algorithms under translation 344
Invariant, Ermakov 152
Invariant, Lewis 152
Invariant, Riemann 181
Inverse transformation 64 171
Involutory transformation 17 64
Jump conditions, Rankine — Hugoniot 254 255
Kadomtsev — Petviashvili equation see “Equation”
Korteweg — de Vries equation see “Equation”
Law, Blatz-Ko 204
Lewis invariant 152
Lie algebra, terminology 390—392
Liouville equation see “Equation”
Materials, harmonic 199 203
Materials, ideally hard 175
Materials, ideally soft 176
Materials, Mooney — Rivlin see “Mooney — Rivlin material”
Metal, simple 20—30
Mooney — Rivlin material 164
Mooney — Rivlin material, Adkins’ duality principle 204—210
Mooney — Rivlin material, arbitrary periodic loading 168 169
Mooney — Rivlin material, blast loading 166—169
Mooney — Rivlin material, free oscillations 165
Mooney — Rivlin material, Heaviside step loading 166
Mooney — Rivlin material, large amplitude oscillation 155—169
Mooney — Rivlin material, plane strain deformation 204—210
Moving boundary problems, conditions on 98—104
Moving boundary problems, constant speed 242—246
Moving boundary problems, invariant boundaries 241—246
Moving boundary problems, nonlinear heat conduction 106—111
Moving boundary problems, single-phase 117 118
Moving boundary problems, solved by inverse method 245 246
Moving boundary problems, Stefan-type 90—92
Navier — Stokes equations 308—311
Navier — Stokes equations, finite groups 310
Navier — Stokes equations, generators 309
Navier — Stokes equations, laminar flow between rotating cylinders 312—314
Navier — Stokes equations, solution independent of viscosity 313
Navier — Stokes equations, stream function form 312
Navier — Stokes equations, symmetry reduction 311
Neumann problem 104 105
Newtonian mechanics, invariance of, under dilation 247
Newtonian mechanics, invariance of, under rotation 247
Newtonian mechanics, invariance of, under translation 247
Newton’s Law of Cooling 132
Ordinary differential equations, group analysis 314—323
Ordinary differential equations, group analysis, Blasius equation 318—323
Ordinary differential equations, group analysis, canonical coordinates 320—322
Ordinary differential equations, group analysis, conversion of boundary value to initial value problems 323—330
Ordinary differential equations, group analysis, determining equations 316—318
Ordinary differential equations, group analysis, eigenvalues 330—340
Ordinary differential equations, group analysis, Emden — Fowler equations 318
Ordinary differential equations, group analysis, exact shooting 325—330
Ordinary differential equations, group analysis, nth-order extension of generator 316
Ordinary differential equations, group analysis, second-order equation 317 318
Ordinary differential equations, group analysis, symmetry reduction 321
Oscillations, large amplitude 155—169
Parameters, shallow water 288
Pinney’s equation 154
Pinney’s equation, canonical coordinates 389
Pinney’s equation, companion 388
Pinney’s equation, nonlinear superposition 387—389
Porous reservoir, two-phase flow 37—48
Potential Kadomtsev — Petviashvili equation 279
Potential Kadomtsev — Petviashvili equation, Backlund transformation 281
Potential Kadomtsev — Petviashvili equation, Bianchi diagram 282
Potential Kadomtsev — Petviashvili equation, generators 278
Potential Kadomtsev — Petviashvili equation, kink solution 283
Potential Kadomtsev — Petviashvili equation, nonlinear superposition 282
Potential Kadomtsev — Petviashvili equation, soliton solution 283
Potential Kadomtsev — Petviashvili equation, splitons 284
Potential modified Kadomtsev — Petviashvili equation 284
Potential modified Kadomtsev — Petviashvili equation, generators 285
Potentials, strain energy, geo 79
Potentials, strain energy, Holden 191
Potentials, strain energy, parametric 189—204
Power law fluids 247
Radiation condition on moving boundary 32
Radiation condition, black body 38
Reaction problem, spherical 117—123
Reciprocal theorem, Adkins’ 207
Reciprocal theorem, Adkins’, bending curved block 207—209
Reciprocal theorem, Adkins’, reciprocal deformation of Mooney — Rivlin materials 209 210
Reciprocal transformation 16—20 31 56 63 113 114
Reciprocal transformation with Backlund transformation 33—37
Reciprocal transformation, atmospheric frontogenesis 76—88
Reciprocal transformation, nonlinear hyperbolic equation 50 51
Reciprocal transformation, visco-elastic waves 53—61
Relation, Faa de Bruno 100
Relation, stress-strain Lagrangian 202
Riccati, equation 174
Riccati, transformation 307
Riemann invariants 181
Robin-type boundary condition 131
Rotating shallow liquid motion, circular shape 295
Rotating shallow liquid motion, commutator table 296
Rotating shallow liquid motion, elliptic shape 294
Rotating shallow liquid motion, generators 292
Rotating shallow liquid motion, group analysis 285—308
Series, Tao 94—104
Shallow water waves 61—76
Shock propagation, group analysis 251—263
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