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Georgescu A. Ч Asymptotic Treatment of Differential Equations (Applied Mathematics)
Georgescu A. Ч Asymptotic Treatment of Differential Equations (Applied Mathematics)



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Ќазвание: Asymptotic Treatment of Differential Equations (Applied Mathematics)

јвтор: Georgescu A.

јннотаци€:

The main definitions and results of asymptotic analysis and the theory 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/

—татус предметного указател€: √отов указатель без номеров страниц

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 274

ƒобавлена в каталог: 01.07.2020

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 "Regularization method"
Asymptotic accumulation point      2 5
Asymptotic analysis      1 3Ч5
Asymptotic approximation of the Navier Ч Stokes model      198Ч231
Asymptotic approximation second order      212Ч213
Asymptotic approximation 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
Bernoulli's equation      210
Bessel functions      15 30 107 226
Bessel's equation      44
Boltzmann's equation      63 233Ч243
Boltzmann's model      233Ч243
Boundary dynamical      206 210 211
Boundary elastic      250
Boundary inner      138Ч141
Boundary layer      50 51 63 70Ч81 74 89 91 115Ч144 143 200Ч212
Boundary mathematical      207 211Ч212
Boundary position      188
Boundary proper      141
Boundary theory      199Ч212
Boundary thickness      77 122 188 211Ч212 250
Boundary type      205
Boundary type functions      124Ч131 135 138 190
Boundary type inner variable      204
Boundary type, boundary (wall) conditions      220Ч222
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 Poincar$\' e$      18
Divergent asymptotic expansions Stieltjes      18
Domain decomposition      116
Domain of validity      12 78Ч79 83 90 92 101 103 104
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
equation      44
equation      44
Equivalence relations      31
Equivalent sequences      11
Erdelyi's theorem      142
Error, order of      13
Euler transform method      37
Euler Ч Maclaurin formula      32
Euler's equation      44 81 147 207Ч208
Euler's model      59 60 61 108 198 206 213 237
Euler's order relations      5
Existence and uniqueness results      223Ч225
Existence interval      68
Existence uniqueness and regularity theorem      67
Expansions intermediate      194Ч195
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
Friedrich's example      183Ч189 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 matching      84Ч100
Global limit      108
Goldstein wave solutions      82
Green's functions      223 242
Gronwall lemma      172
Hausdorff      2
Hausdorff      2
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
InitialЧvalue 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 of finite order rank of      44
Kaplun's extension lemma      105Ч106
Kaplun's methods      102Ч109 104
Kaplun's optimal coordinates      177
Knudsen dimensionless      224
Knudsen numbers      232Ч243
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
Lagrange's methods      164 172
Lam$\' e$ equation      44
Laplace method of saddle points      28 49
Laurent series      43
leading term of      13
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      106Ч108
Limits local      108
Limits main      107
Limits outer      106
Limits problem      208
Limits process expansion      41
Limits solution      76
Lindstedt Ч Poincar$\' e$ method      110Ч112
Linear equations with large parameters      45
Lipschitz condition      172
Lipschitz functions      64 67Ч68 120
local variables      108
Lomov's raising method      137
Matching $n \times m$      82Ч84 88Ч89 91Ч100 102 104 106 134 212
Matching 1 $\times$ 1      87Ч91 132 134 210
Matching general      84Ч100
Matching intermediate      97 102 189Ч197
Matching principle      79Ч80
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      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
Na$\" i$ve 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) nonЧhomogeneous      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
Pad$\' e$ 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
Poincar$\' e$      18 31
Poincar$\' e$ definition      103
Poincar$\' e$ expansions      84 158
Poincar$\' e$ 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      55 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 phenomena      45Ч53
Resonance singular equations      56
Resonance singular equations      56
Resonance singular equations      56
Resonance singular equations      56
Reversion of series method      37
Reversion of series method      37
Reynolds number (Re)      54 58 60 73 83 160 176 185Ч186
Reynolds number (Re)      54 58 60 73 83 160 176 185Ч186
Reynolds number (Re) large      198Ч213
Reynolds number (Re) large      198Ч213
Reynolds number (Re) large      198Ч213
Reynolds number (Re) large      198Ч213
Reynolds number (Re) small      213Ч231
Reynolds number (Re) small      213Ч231
Reynolds number (Re) small      213Ч231
Reynolds number (Re) small      213Ч231
Riemannian method of steepest descent      28Ч29 49
Riemannian method of steepest descent      28Ч29 49
Riemannian surface      15
Riemannian surface      15
Secular problems      70Ч75 81
1 2
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