|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Georgescu A. — Asymptotic Treatment of Differential Equations |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Airy equation 15 48 49
AntiStokes line 15
Artificial viscosity method see “Regularization method”
Asymptotic, accumulation point 2 5
Asymptotic, analysis 1 3—5
Asymptotic, approximation of the Navier — Stokes model 198—231
Asymptotic, approximation of the Navier — Stokes model, second order 212—213
Asymptotic, approximation of the Navier — Stokes model, theory 2 3—5 18—20 27 32 58 62 69
Asymptotic, equality 31
Asymptotic, expansions 3 12—30 62 72 73
Asymptotic, expansions, Cheaplygin 39
Asymptotic, expansions, composite 101—102 114
Asymptotic, expansions, contained 101
Asymptotic, expansions, convergent 38
Asymptotic, expansions, defined by an integral 28—30
Asymptotic, expansions, differentiation 21
Asymptotic, expansions, divergent 18
Asymptotic, expansions, double 21
Asymptotic, expansions, inner 78—81 92 100 131—137 145 176 197 204—213 218
Asymptotic, expansions, intermediate 94 100
Asymptotic, expansions, operations with 20—22
Asymptotic, expansions, outer 77—81 92 100 131—137 145 176 197 204—213 218
Asymptotic, expansions, regular 56
Asymptotic, expansions, significant 101
Asymptotic, expansions, uniform 48 100
Asymptotic, expansions, varying slowly, quickly 48
Asymptotic, parameters 2
Asymptotic, power series 14
Asymptotic, representation 13
Asymptotic, sequences 2 10—11 16 22—28
Asymptotic, sequences, multiplicative 21
Asymptotic, sequences, solution 63
Asymptotic, sequences, variables 2
Asymptotic, series, divergent 38
Asymptotic, series, intermediate 97
Asymptotic, series, representation 3
Asymptotic, series, summation 32
Averaged formulation 64—65
Averaging methods 164—175
Banach space 236
Bernoulli’s equation 210
Bessel functions 15 30 107 226
Bessel’s equation 44
Boltzmann’s equation 63 233—243
Boltzmann’s model 233—243
Boundary layer 50 51 63 70—81 74 89 91 115—144 143 200—212
Boundary layer, dynamical 206 210 211
Boundary layer, elastic 250
Boundary layer, inner 138—141
Boundary layer, mathematical 207 211—212
Boundary layer, position 188
Boundary layer, proper 141
Boundary layer, theory 199—212
Boundary layer, thickness 77 122 188 211—112 250
Boundary layer, type 205
Boundary layer, type, boundary (wall) conditions 220—222
Boundary layer, type, functions 124—131 135 138 190
Boundary layer, type, inner variable 204
Burgers turbulence model 57
Cahn — Hillard equations 148
Cauchy problem 57—58 63—64 67 136 145 162 164 235
Changing type equations 71
Characteristic force 199
Cheaplygin asymptotic series 39
Completion of series 37
Consistent expansion 16
Constants variaion, formula of 171
Continuity equation 209 224
Contour integrals 28
Convergence, improvement 32
Convergence, radius of 35
Convergent, factors 32—39
Convergent, series 35 38 39 58
Coordinates, optimal 108—109
Coordinates, stretched 109—113
Couette plane basic flow 49
Crude formulation 65
Degenerate problem 55 58
Derivative expansion method 157
Determinantal equation 44
Dimensional pressure 62 213
Dimensionless quantities 60—62 205
Dirac function 242
Divergent asymptotic expansions 18 38
Divergent asymptotic expansions, Emde 18
Divergent asymptotic expansions, Poincare 18
Divergent asymptotic expansions, Stieltjes 18
Domain of validity 12 78—79 83 90 92 101 103 104
Domain, decomposition 116
Domain, overlapping 78—79 105—106
Domain, unbounded 23 144
Domb — Sykes plot 36 37
Double scale method 147 148 155
Double scale method, generalized 156
Duffing equation 112 153 166—167 169
Elastic behaviour 249—251
Elastic boundary layer 250
Enskog method 241—242
Equivalence relations 31
Equivalent sequences 11
Erdelyi’s theorem 142
Error, order of 13
Euler transform method 37
Euler — Maclaurin formula 32
Euler’s, equation 44 81 147 207—208
Euler’s, equation, model 59 60 61 108 198 206 213 237
Euler’s, equation, order relations 5
Existence and uniqueness results 223—225
Existence, interval 68
Existence, uniqueness and regularity theorem 67
Expansions, intermediate 194—195
Expansions, leading term of 13
Extraction of additive singularity 37
Extraction of multiplicative singularity 37
Far Field condition 13 61 65—67 210 214 220 222—223
Fixed function 7
Flexural rigidity 249
Fluid turbulence 65
Forces, characteristic 199
Forces, inertial 199
Forces, viscous 199 210
Formula of constants variation 171
Fourier, expansion 167
Fourier, series 164
Fourier, transform 237
Fredholm equations 144
Friedrich’s, example 183—189 184
Friedrich’s, model 206
Fuchs equation 43 44
Functions, fixed 7
Functions, gauge 11
Functions, standard 11
Functions, very large 7
Functions, very small 7
Gauge Functions 11 18 40
Gauss’s equation 44
General matchi ng 84—100
Global limit 108
Goldstein wave solutions 82
Green’s functions 223 242
Gronwall lemma 172
Hausdorff topological space 2
Heisenberg — Lin solution 58
Hele — Shaw, creeping flow 222
Hele — Shaw, motion 220—223
Hele — Shaw, solution 223
Hilbert, analysis 239
Hilbert, space 235
Holomorphic functions 43 44
Holomorphic solutions 42
| Homogenization method 163—164
Homogenized equation 163
Hydrology 244 249
Hyperasymptotics 28
Incompressible fluids 200
Inertia terms 61 203
Inertial force 199
Initial-value problems 116—137
Inner, transition layer 141
Inner, variable 75
Intermediate expansions 194—195
Intermediate limit 195
Intermediate matching 82 197
Intermediate principles 195 197
Intermediate region 218
Intermediate series 97 133
Intermediate variables 218
irregular singular points 44
Irregular singular points of finite order 44
Irregular singular points, rank of 44
Kaplun’s extension lemma 105—106
Kaplun’s methods 102—109 104
Kaplun’s optimal coordinates 177
Knudsen numbers 232—243
Knudsen numbers, dimensionless 224
Krylov and Bogoliubov, method of 167—168 172
Krylov — Bogoliubov — Mitropolski method 168—169 173
Lagerstrom, example 60 176 189—197 229—230
Lagerstrom, model 214 216 223
Lagerstrom, variant 194
Lagrange’s methods 164 172
Lame equation 44
Laplace method of saddle points 28 49
Laurent series 43
Legendre’s equation 4
Liapunov stability 137 252
Lighthill method of stretched coordinates 113
Limits, degenerate equation 55 77
Limits, equations 208
Limits, inner 106
Limits, intermediate 106—108
Limits, local 108
Limits, main 107
Limits, outer 106
Limits, problem 208
Limits, process expansion 41
Limits, solution 76
Lindstedt — Poincare method 110—112
Linear equations with large parameters 45
Lipschitz condition 172
Lipschitz functions 64 67—68 120
local variables 108
Lomov’s raising method 137
Matching,  87—91 132 134 210
Matching,  82—84 88—89 91—100 102 104 106 134 212
Matching, general 84—100
Matching, intermediate 97 102 189—197
Matching, principle 79—80
Materials, strength of 252
Mathieu’s equation 44
Maxwell distribution 234 239
Maxwell molelcular chaos hypothesis 235
Mechanics, non-linear 252
Memory term 163
Meteorology 244—245
Motion, past a cylinder 213—220 222
Motion, past a sphere 220—223
Multiple, deck method 82 83
Multiple, scale method 144—164
Multiple, variable method 156
Multiplicative asymptotic sequences 21
Multiplicative asymptotic series 22
Naive formulation 63—65 76 79 119
Navier — Stokes equations 44 58 61 81 82—83 108 188 201
Navier — Stokes model (NSm) 176 185 186 189
Navier — Stokes model (NSm) at large Reynolds number 198—213
Navier — Stokes model (NSm) at small Reynolds number 213—231
Navier — Stokes model (NSm), non-homogeneous 241
Navier — Stokes — Fourier model 86 242
Non-uniformity region 70 75
Oblique asymptotes 17
Olmstead — Gantesen paradox 222
Optimal coordinates 108—109
Optimum meshes 115—116
Order functions 40
Order relations 2 5—10
Orr — Sommerfeld equation 48—49 57 160
Oseen, equations 229
Oseen, model 185—186 189 223—231
Oseen, problem 217 220
Oseen, solution 222
Pade approximants 37
Passage to the limit theorem 68 121
Periodic cylinder function 52
Perturbation, equations 55 61
Perturbation, theory 1 40 41
Perturbed mapping 55
Physical parameters 2
Poincare 18 31
Poincare, definition 103
Poincare, expansions 84 158
Poincare, form 40
Poisson formula 32
Pole of even order 46
Power, sequences 17
Power, series 3 22
Prandtl, boundary 177
Prandtl, dynamic boundary layer 91
Prandtl, equation 209
Prandtl, method 81—82 108 176—183
Prandtl, model (Pm) 186—188 201 206 213
Pressure gradient 203
Radius of convergence 35
Rapid variation 56 76
Rayleigh equation 44 57 58
Recurrence relations 13
Reduced equation 57
Reduced problem 5 5 57 58 77 208 222
Regular perturbations 25 26
Regular point for equation 42 43
Regularization method 55
Relative fluid velocity 199
Remainder expansions 12
Resonance, phenomena 45—53
Resonance, singular equations 56
Reversion of series method 37
Reynolds number (Re) 54 58 60 73 83 160 176 185—186
Reynolds number (Re), large 198—213
Reynolds number (Re), small 213—231
Riemannian method of steepest descent 28—29 49
Riemannian surface 15
Secular problems 70—75 81
Secular term 41 110
Sequences, equivalent 11
Series intermediate 97 133
Shanks transform 37
Shock layer see “Inner transition layer”
Singular perturbation 28 47 49—50
Singular points 3 44 46
Singularity of equations 27 41—45
Small parameters 60—62 70
Small parameters, integro-differential equations with 144
Small parameters, two-point conditions 142—144
Standard functions 11
Stieltjes 18 31
Stirling’s formula 4 32
Stokes, equation 44
Stokes, lines 14 30
Stokes, method of stationary phases 28
Stokes, model 176 186 189 223—231
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå