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Georgescu A. Ч Asymptotic Treatment of Differential Equations
Georgescu A. Ч Asymptotic Treatment of Differential Equations

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Ќазвание: Asymptotic Treatment of Differential Equations

јвтор: Georgescu A.

јннотаци€:

The main definitions and results of asymptotic analysis and thetheory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity.
Due to the generality of presentation this applications-oriented book is suitable for the solving of differential equations from any other field of interest.


язык: en

–убрика: ћатематика/јнализ/јсимптотические методы, “еори€ возмущений/

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

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 272

ƒобавлена в каталог: 02.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Airy equation      15 48 49
AntiStokes line      15
Artificial viscosity method      see УRegularization methodФ
Asymptotic, accumulation point      2 5
Asymptotic, analysis      1 3Ч5
Asymptotic, approximation of the Navier Ч Stokes model      198Ч231
Asymptotic, approximation of the Navier Ч Stokes model, second order      212Ч213
Asymptotic, approximation of the Navier Ч Stokes model, theory      2 3Ч5 18Ч20 27 32 58 62 69
Asymptotic, equality      31
Asymptotic, expansions      3 12Ч30 62 72 73
Asymptotic, expansions, Cheaplygin      39
Asymptotic, expansions, composite      101Ч102 114
Asymptotic, expansions, contained      101
Asymptotic, expansions, convergent      38
Asymptotic, expansions, defined by an integral      28Ч30
Asymptotic, expansions, differentiation      21
Asymptotic, expansions, divergent      18
Asymptotic, expansions, double      21
Asymptotic, expansions, inner      78Ч81 92 100 131Ч137 145 176 197 204Ч213 218
Asymptotic, expansions, intermediate      94 100
Asymptotic, expansions, operations with      20Ч22
Asymptotic, expansions, outer      77Ч81 92 100 131Ч137 145 176 197 204Ч213 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 10Ч11 16 22Ч28
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      64Ч65
Averaging methods      164Ч175
Banach space      236
BernoulliТs equation      210
Bessel functions      15 30 107 226
BesselТs equation      44
BoltzmannТs equation      63 233Ч243
BoltzmannТs model      233Ч243
Boundary layer      50 51 63 70Ч81 74 89 91 115Ч144 143 200Ч212
Boundary layer, dynamical      206 210 211
Boundary layer, elastic      250
Boundary layer, inner      138Ч141
Boundary layer, mathematical      207 211Ч212
Boundary layer, position      188
Boundary layer, proper      141
Boundary layer, theory      199Ч212
Boundary layer, thickness      77 122 188 211Ч112 250
Boundary layer, type      205
Boundary layer, type, boundary (wall) conditions      220Ч222
Boundary layer, type, functions      124Ч131 135 138 190
Boundary layer, type, inner variable      204
Burgers turbulence model      57
Cahn Ч Hillard equations      148
Cauchy problem      57Ч58 63Ч64 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      32Ч39
Convergent, series      35 38 39 58
Coordinates, optimal      108Ч109
Coordinates, stretched      109Ч113
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      60Ч62 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 78Ч79 83 90 92 101 103 104
Domain, decomposition      116
Domain, overlapping      78Ч79 105Ч106
Domain, unbounded      23 144
Domb Ч Sykes plot      36 37
Double scale method      147 148 155
Double scale method, generalized      156
Duffing equation      112 153 166Ч167 169
Elastic behaviour      249Ч251
Elastic boundary layer      250
Enskog method      241Ч242
Equivalence relations      31
Equivalent sequences      11
ErdelyiТs theorem      142
Error, order of      13
Euler transform method      37
Euler Ч Maclaurin formula      32
EulerТs, equation      44 81 147 207Ч208
EulerТs, equation, model      59 60 61 108 198 206 213 237
EulerТs, equation, order relations      5
Existence and uniqueness results      223Ч225
Existence, interval      68
Existence, uniqueness and regularity theorem      67
Expansions, intermediate      194Ч195
Expansions, leading term of      13
Extraction of additive singularity      37
Extraction of multiplicative singularity      37
Far Field condition      13 61 65Ч67 210 214 220 222Ч223
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
FriedrichТs, example      183Ч189 184
FriedrichТs, 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
GaussТs equation      44
General matchi ng      84Ч100
Global limit      108
Goldstein wave solutions      82
GreenТs functions      223 242
Gronwall lemma      172
Hausdorff topological space      2
Heisenberg Ч Lin solution      58
Hele Ч Shaw, creeping flow      222
Hele Ч Shaw, motion      220Ч223
Hele Ч Shaw, solution      223
Hilbert, analysis      239
Hilbert, space      235
Holomorphic functions      43 44
Holomorphic solutions      42
Homogenization method      163Ч164
Homogenized equation      163
Hydrology      244 249
Hyperasymptotics      28
Incompressible fluids      200
Inertia terms      61 203
Inertial force      199
Initial-value problems      116Ч137
Inner, transition layer      141
Inner, variable      75
Intermediate expansions      194Ч195
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
KaplunТs extension lemma      105Ч106
KaplunТs methods      102Ч109 104
KaplunТs optimal coordinates      177
Knudsen numbers      232Ч243
Knudsen numbers, dimensionless      224
Krylov and Bogoliubov, method of      167Ч168 172
Krylov Ч Bogoliubov Ч Mitropolski method      168Ч169 173
Lagerstrom, example      60 176 189Ч197 229Ч230
Lagerstrom, model      214 216 223
Lagerstrom, variant      194
LagrangeТs methods      164 172
Lame equation      44
Laplace method of saddle points      28 49
Laurent series      43
LegendreТs 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      106Ч108
Limits, local      108
Limits, main      107
Limits, outer      106
Limits, problem      208
Limits, process expansion      41
Limits, solution      76
Lindstedt Ч Poincare method      110Ч112
Linear equations with large parameters      45
Lipschitz condition      172
Lipschitz functions      64 67Ч68 120
local variables      108
LomovТs raising method      137
Matching, $1\times 1$      87Ч91 132 134 210
Matching, $n\times m$      82Ч84 88Ч89 91Ч100 102 104 106 134 212
Matching, general      84Ч100
Matching, intermediate      97 102 189Ч197
Matching, principle      79Ч80
Materials, strength of      252
MathieuТs equation      44
Maxwell distribution      234 239
Maxwell molelcular chaos hypothesis      235
Mechanics, non-linear      252
Memory term      163
Meteorology      244Ч245
Motion, past a cylinder      213Ч220 222
Motion, past a sphere      220Ч223
Multiple, deck method      82 83
Multiple, scale method      144Ч164
Multiple, variable method      156
Multiplicative asymptotic sequences      21
Multiplicative asymptotic series      22
Naive formulation      63Ч65 76 79 119
Navier Ч Stokes equations      44 58 61 81 82Ч83 108 188 201
Navier Ч Stokes model (NSm)      176 185 186 189
Navier Ч Stokes model (NSm) at large Reynolds number      198Ч213
Navier Ч Stokes model (NSm) at small Reynolds number      213Ч231
Navier Ч Stokes model (NSm), non-homogeneous      241
Navier Ч Stokes Ч Fourier model      86 242
Non-uniformity region      70 75
Oblique asymptotes      17
Olmstead Ч Gantesen paradox      222
Optimal coordinates      108Ч109
Optimum meshes      115Ч116
Order functions      40
Order relations      2 5Ч10
Orr Ч Sommerfeld equation      48Ч49 57 160
Oseen, equations      229
Oseen, model      185Ч186 189 223Ч231
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      81Ч82 108 176Ч183
Prandtl, model (Pm)      186Ч188 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      45Ч53
Resonance, singular equations      56
Reversion of series method      37
Reynolds number (Re)      54 58 60 73 83 160 176 185Ч186
Reynolds number (Re), large      198Ч213
Reynolds number (Re), small      213Ч231
Riemannian method of steepest descent      28Ч29 49
Riemannian surface      15
Secular problems      70Ч75 81
Secular term      41 110
Sequences, equivalent      11
Series intermediate      97 133
Shanks transform      37
Shock layer      see УInner transition layerФ
Singular perturbation      28 47 49Ч50
Singular points      3 44 46
Singularity of equations      27 41Ч45
Small parameters      60Ч62 70
Small parameters, integro-differential equations with      144
Small parameters, two-point conditions      142Ч144
Standard functions      11
Stieltjes      18 31
StirlingТs formula      4 32
Stokes, equation      44
Stokes, lines      14 30
Stokes, method of stationary phases      28
Stokes, model      176 186 189 223Ч231
1 2
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