Georgescu A. — Asymptotic Treatment of Differential Equations (Applied Mathematics) :: Электронная библиотека попечительского совета мехмата МГУ

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

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Название: Asymptotic Treatment of Differential Equations (Applied Mathematics)

Автор: Georgescu A.

Аннотация:

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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 274

Добавлена в каталог: 01.07.2020

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Предметный указатель

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 second order      212—213
Asymptotic approximation 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 dynamical      206 210 211
Boundary elastic      250
Boundary inner      138—141
Boundary layer      50 51 63 70—81 74 89 91 115—144 143 200—212
Boundary mathematical      207 211—212
Boundary position      188
Boundary proper      141
Boundary theory      199—212
Boundary thickness      77 122 188 211—212 250
Boundary type      205
Boundary type functions      124—131 135 138 190
Boundary type inner variable      204
Boundary type, boundary (wall) conditions      220—222
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 Poincar $\' e$       18
Divergent asymptotic expansions Stieltjes      18
Domain decomposition      116
Domain of validity      12 78—79 83 90 92 101 103 104
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
equation      44
equation      44
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 model      59 60 61 108 198 206 213 237
Euler's order relations      5
Existence and uniqueness results      223—225
Existence interval      68
Existence uniqueness and regularity theorem      67
Expansions intermediate      194—195
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 matching      84—100
Global limit      108
Goldstein wave solutions      82
Green's functions      223 242
Gronwall lemma      172
Hausdorff      2
Hausdorff      2
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 of finite order rank of      44
Kaplun's extension lemma      105—106
Kaplun's methods      102—109 104
Kaplun's optimal coordinates      177
Knudsen dimensionless      224
Knudsen numbers      232—243
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
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      106—108
Limits local      108
Limits main      107
Limits outer      106
Limits problem      208
Limits process expansion      41
Limits solution      76
Lindstedt — Poincar $\' e$ 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 $n \times m$       82—84 88—89 91—100 102 104 106 134 212
Matching 1 $\times$ 1      87—91 132 134 210
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
Na $\" i$ ve 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
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      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      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      45—53
Resonance phenomena      45—53
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 83 160 176 185—186
Reynolds number (Re)      54 58 60 73 83 160 176 185—186
Reynolds number (Re) large      198—213
Reynolds number (Re) large      198—213
Reynolds number (Re) large      198—213
Reynolds number (Re) large      198—213
Reynolds number (Re) small      213—231
Reynolds number (Re) small      213—231
Reynolds number (Re) small      213—231
Reynolds number (Re) small      213—231
Riemannian method of steepest descent      28—29 49
Riemannian method of steepest descent      28—29 49
Riemannian surface      15
Riemannian surface      15
Secular problems      70—75 81

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