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Rogers C., Ames W.F. Ч Nonlinear boundary value problems in science and engineering
Rogers C., Ames  W.F. Ч Nonlinear boundary value problems in science and engineering



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Ќазвание: Nonlinear boundary value problems in science and engineering

јвторы: Rogers C., Ames W.F.

язык: en

–убрика: ћатематика/„исленные методы/„исленный анализ/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 215

ƒобавлена в каталог: 25.02.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Acceleration, potential, TruesdellТs      161
Algebra, Lie,      238Ч240
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      390Ч392
Algebra, Lie, Jacobi identity      239
Atmospheric frontogenesis      76Ч88
Backlund transformation      2 3 14
Backlund transformation with reciprocal transformation      33Ч37
Backlund transformation, Loewner-type      169 170
Backlund transformation, reciprocal      107
Backlund transformation, strong      151
Backlund transformation, weak      150 152
Bergman expansion      92 98 124Ч145
Bergman expansion, Pade extension      134Ч145
Bergman expansion, termination      179Ч189
Bergman integral operator method      180
Boundaries, invariant      241
Boundaries, invariant, heat equation      241Ч246
Boundaries, invariant, Stefan-type, moving      241Ч246
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 Ч Boltzmann type      133
Boundary value problems, nonlinear, BurgersТ hierarchy      5Ч11
Boundary value problems, nonlinear, conservation law      16
Boundary value problems, nonlinear, coupled reciprocal and Backlund transformation      33Ч37
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      9Ч11
Boundary value problems, nonlinear, spherical      134 135
Boundary value problems, nonlinear, Stefan Ч Boltzmann      134Ч135
Boussinesq, equation      278
Boussinesq, fluid      82
Burgers, equation      45
Burgers, hierarchy      9 36
Canonical coordinates, group analysis      320Ч322
Canonical coordinates, Riemann Ч Volterra      14
Cauchy Ч 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, NewtonТs law      132
Dilation (dilation or scaling) group      247 248
Dilation (dilation or scaling) group, invariants      249
Duality principle, AdkinsТ      205
Elastic materials, deformation, finite plane strain      189Ч204
Elastic materials, deformation, homogeneous strain      197 198
Elastic materials, deformation, twisting of circular hole      198 199
Elasticity, nonlinear, group analysis      263Ч270
Elasticity, nonlinear, group generators      265
Equations, Boussinesq      278
Equations, Burgers      5
Equations, Cauchy Ч Riemann      203
Equations, Ermakov      150Ч155
Equations, evolution      19
Equations, heat conduction      5 239
Equations, hydrodynamic      61
Equations, Kadomtsev Ч Petviashvili      276
Equations, Kadomtsev Ч Petviashvili, potential      279
Equations, Korteweg Ч de Vries, linear      10
Equations, Korteweg Ч de Vries, nonlinear      278
Equations, Liouville      2 3 185
Equations, Monge Ч Ampere      4
Equations, Pinney      154
Equations, Riccati      174
Equations, Stokes Ч Beltrami      65
Equilibrium equations, Lagrangian      200
Ermakov invariant      152
Ertel potential vorticity      84
Exact shooting, boundary value problems      325Ч330
Exact shooting, eigenvalue problems      330Ч340
Exact shooting, examples      328Ч330 333Ч340
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      92Ч98
Expansion, Tao type      94Ч104
Faa de BrunoТs relation      100 120
Falkner Ч Skan flow      250
Flow, two-phase      37Ч48
Fokker Ч Planck equation      see УEquationФ
Forsyth Ч Hopf Ч Cole transformation      6Ч9 13 46
Frontogenesis equation, reduced to linear      86
Gas law, Karman Ч Tsien-type      147
Gas law, Prim-type      77 78
Geo potential      79
Group analysis, Lie invariance, boundary layer      246Ч251
Group analysis, Lie invariance, calculation near singularity      340Ч342
Group analysis, Lie invariance, canonical variables      320Ч322
Group analysis, Lie invariance, construction of      213Ч226
Group analysis, Lie invariance, determining equations      220Ч223
Group analysis, Lie invariance, Euler equations      309
Group analysis, Lie invariance, finite differences      342Ч344
Group analysis, Lie invariance, generator and extensions      220Ч223
Group analysis, Lie invariance, infinitesimal transformations      216
Group analysis, Lie invariance, invariant solution      224
Group analysis, Lie invariance, Kadomtsev Ч Petviashvili      276Ч279
Group analysis, Lie invariance, Korteweg Ч de Vries      275 276
Group analysis, Lie invariance, Navier Ч Stokes      308Ч311
Group analysis, Lie invariance, nonlinear elasticity      263Ч270
Group analysis, Lie invariance, ordinary differential equation, second-order      314Ч323
Group analysis, Lie invariance, partial differential equation, second-order      215Ч226
Group analysis, Lie invariance, potential Kadomtsev Ч Petviashvili      279
Group analysis, Lie invariance, potential modified Kadomtsev Ч Petviashvili      284 285
Group analysis, Lie invariance, reacting flows      251Ч263
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      271Ч274 (see also УGroup generatorsФ)
Group generators, for equations, axially symmetric wave      362
Group generators, for equations, baroclinic layer      376
Group generators, for equations, Blasius      318Ч323
Group generators, for equations, boundary layer, power law      246Ч251
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      371Ч373
Group generators, for equations, boundary layer, two-dimensional with moment stresses      373
Group generators, for equations, Boussinesq-type      354 355
Group generators, for equations, BurgersТ potential      348 349
Group generators, for equations, Davey Ч 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      263Ч270
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      349Ч351
Group generators, for equations, Jimbo Ч Miwa      358
Group generators, for equations, Kadomtsev Ч Petviashvili      276Ч279
Group generators, for equations, Kadomtsev Ч Petviashvili, generalized cylindrical      357 358
Group generators, for equations, Kadomtsev Ч Petviashvili, potential      279
Group generators, for equations, Kadomtsev Ч Petviashvili, potential modified      284 285
Group generators, for equations, Korteweg Ч de Vries      275 276
Group generators, for equations, Korteweg Ч de Vries Ч 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 Ч Stokes      308Ч311
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      251Ч263
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 Ч Tsien      373 374
Group generators, for equations, transonic, steady      375 376
Group generators, for equations, von Karman      271Ч274
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      123Ч133
Heat conduction, nonlinear, invariant finite differences      342Ч344
Heat conduction, nonlinear, similarity solution      92
Heat conduction, nonlinear, simple metals      20Ч30
Heat conduction, nonlinear, single phase moving boundary      106Ч111
Heat conduction, nonlinear, solid hydrogen      30Ч33
Heat conduction, nonlinear, two-phase Stefan problem      111Ч117
Hodograph      170 172 179
Hydrodynamic equations      61
Hydrogen, solid heat conduction      30Ч33
Hydrostatic approximation      79
Hyperbolic equation      50
Hyperbolic equation, reciprocal transformation      50
Hyperelastic material      154Ч157
Hyperelastic material, stress tensor      156
Inequality, Rivlin Ч Saunders      163
Infiltration, with prescribed flux      11Ч14
Initial value problem, Cauchy      179Ч189
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 Ч Hugoniot      254 255
Kadomtsev Ч Petviashvili equation      see УEquationФ
Korteweg Ч de Vries equation      see УEquationФ
Law, Blatz-Ko      204
Lewis invariant      152
Lie algebra, terminology      390Ч392
Liouville equation      see УEquationФ
Materials, harmonic      199 203
Materials, ideally hard      175
Materials, ideally soft      176
Materials, Mooney Ч Rivlin      see УMooney Ч Rivlin materialФ
Metal, simple      20Ч30
Mooney Ч Rivlin material      164
Mooney Ч Rivlin material, AdkinsТ duality principle      204Ч210
Mooney Ч Rivlin material, arbitrary periodic loading      168 169
Mooney Ч Rivlin material, blast loading      166Ч169
Mooney Ч Rivlin material, free oscillations      165
Mooney Ч Rivlin material, Heaviside step loading      166
Mooney Ч Rivlin material, large amplitude oscillation      155Ч169
Mooney Ч Rivlin material, plane strain deformation      204Ч210
Moving boundary problems, conditions on      98Ч104
Moving boundary problems, constant speed      242Ч246
Moving boundary problems, invariant boundaries      241Ч246
Moving boundary problems, nonlinear heat conduction      106Ч111
Moving boundary problems, single-phase      117 118
Moving boundary problems, solved by inverse method      245 246
Moving boundary problems, Stefan-type      90Ч92
Navier Ч Stokes equations      308Ч311
Navier Ч Stokes equations, finite groups      310
Navier Ч Stokes equations, generators      309
Navier Ч Stokes equations, laminar flow between rotating cylinders      312Ч314
Navier Ч Stokes equations, solution independent of viscosity      313
Navier Ч Stokes equations, stream function form      312
Navier Ч 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
NewtonТs Law of Cooling      132
Ordinary differential equations, group analysis      314Ч323
Ordinary differential equations, group analysis, Blasius equation      318Ч323
Ordinary differential equations, group analysis, canonical coordinates      320Ч322
Ordinary differential equations, group analysis, conversion of boundary value to initial value problems      323Ч330
Ordinary differential equations, group analysis, determining equations      316Ч318
Ordinary differential equations, group analysis, eigenvalues      330Ч340
Ordinary differential equations, group analysis, Emden Ч Fowler equations      318
Ordinary differential equations, group analysis, exact shooting      325Ч330
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      155Ч169
Parameters, shallow water      288
PinneyТs equation      154
PinneyТs equation, canonical coordinates      389
PinneyТs equation, companion      388
PinneyТs equation, nonlinear superposition      387Ч389
Porous reservoir, two-phase flow      37Ч48
Potential Kadomtsev Ч Petviashvili equation      279
Potential Kadomtsev Ч Petviashvili equation, Backlund transformation      281
Potential Kadomtsev Ч Petviashvili equation, Bianchi diagram      282
Potential Kadomtsev Ч Petviashvili equation, generators      278
Potential Kadomtsev Ч Petviashvili equation, kink solution      283
Potential Kadomtsev Ч Petviashvili equation, nonlinear superposition      282
Potential Kadomtsev Ч Petviashvili equation, soliton solution      283
Potential Kadomtsev Ч Petviashvili equation, splitons      284
Potential modified Kadomtsev Ч Petviashvili equation      284
Potential modified Kadomtsev Ч Petviashvili equation, generators      285
Potentials, strain energy, geo      79
Potentials, strain energy, Holden      191
Potentials, strain energy, parametric      189Ч204
Power law fluids      247
Radiation condition on moving boundary      32
Radiation condition, black body      38
Reaction problem, spherical      117Ч123
Reciprocal theorem, AdkinsТ      207
Reciprocal theorem, AdkinsТ, bending curved block      207Ч209
Reciprocal theorem, AdkinsТ, reciprocal deformation of Mooney Ч Rivlin materials      209 210
Reciprocal transformation      16Ч20 31 56 63 113 114
Reciprocal transformation with Backlund transformation      33Ч37
Reciprocal transformation, atmospheric frontogenesis      76Ч88
Reciprocal transformation, nonlinear hyperbolic equation      50 51
Reciprocal transformation, visco-elastic waves      53Ч61
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      285Ч308
Series, Tao      94Ч104
Shallow water waves      61Ч76
Shock propagation, group analysis      251Ч263
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