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Egorov Y.V. (Ed), Shubin M.A. (Ed) — Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients
Egorov Y.V. (Ed), Shubin M.A. (Ed) — Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

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Название: Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

Авторы: Egorov Y.V. (Ed), Shubin M.A. (Ed)

Аннотация:

The book contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 263

Добавлена в каталог: 13.09.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Agranovich, M.S.      4 6 26 36 37 67 69 113 114 155 156 232 251 252
Airy, G.B.      72 73
Amplitude of Fourier integral operater      49
Amplitude of pseudodifferential operater      9
Amplitude, classical      11
Analytic continuation of generalized function      41
Analytic functional      159
Arnol'd, V.I.      54 82 85 92 114 115 248—251
Atiyah, M.F.      25 109 114 115 127 242—247 250 252
Babich, V.M.      96 114 115
Balaban, T.      67 115
Banach, S.      164 165
Bateman, H.      146 188 199 209 210 251 252
Beals, R.      65 114 115
Beltrami, E.      106 112
Berard, P.H.      113—115
Berezin, F.A.      96 115
Bernshtejn, I.N.      143 167 172 173 250 252
Bers, L.      36 37 115
Bessel, F.W.      125 186 188 193 198 207
Bicharacteristic(s)      63 182
Bicharacteristic(s) strips      182
Bicharacteristic(s), glancing      73
Bicharacteristic(s), null      74
Big singularity      112
Birman, M.Sh.      114 115
Bjork, J.E.      250 252
Bochner, S.      159 166 239
Bogolyubov, N.N.      126 127 144 145 206 251 252
Borovikov, V.A.      248 250 252
Bott, R.      109 114 115 127 242—247 250 252
Boundary value of analytic function      141
Boundary-value problem, regular      221 226
Boundary-value problem, third      225
Boundary-value problem, well-posed      231
Brillouin, L.      78
Buldyrev, V.S.      96 114 115
Bunyakovskij, V.Ya.      154
Calderon, A.P.      36 39 40 43 113 115
Carleman, T.      110 115
Cauchy problem      225
Cauchy problem, regular      226
Cauchy, A.L.      30 31 39 49 62 86 87 140 154 165 166 170 184 218 224 225 227—231 235 238
Caustics      90
Characteristic cone      179 183 242
Characteristic conoid      183
Characteristic conormal      178
Characteristic equation      178
Characteristic hypersurface      179
Characteristic plane      179
Characteristic polynomial      241
Chazarain, J.      111
Colin de verdiere      111
Condition with parameter, ellipticity      26
Condition, Hersh — Kreiss      66
Condition, Sakamato      68
Condition, Shapiro — Lopatinskij      232
Condition, uniform Lopatinskij      69
Cone      138
Cone, dual      160
Cone, future light      203
Cone, light      203
Cone, past light      203
Conical subset      45
Conjecture, Sato      73
Convolution of functions      137
Convolution of generalized functions      137
Cordes, H.O.      115
Courant, R.      96 97 100 115 182 183 251 252
D'Alembert, J.      125 144 237
Davydova, A.M.      248—250 252
Differential form, closed      54
Differential form, non-degenerate      54
Dirac, P.A.M.      129 133 252
Direction, hyperbolic      71
Dirichlet problem      224
Dirichlet problem for operator      229
Dirichlet, L.P.G.      43 99 224 225 229
distribution      128
Distribution with compact support      135
Distribution, exponentially growing      161
Distribution, Fourier      59
Distribution, temperately growing      141
Ditkin, V.A.      176 177 250 252
Division problem      164
Division problem in classes of tempered distributions      167
Doetsch, G.      126 176 177 250
Duistermaat, J.      63 112 114 116
Dynin, A.S.      25
Egorov, Yu.V.      4 6 8 9 13 14 16—19 26 37 40 41 44 48 55 56 61 62 65 67 68 85 90 96 99 101 110 114 116 251 252
Ehjdel'man, S.D. (=eidel'man, S.D.)      237 238 251 252
Ehrenpreis, L.      125 143 164 165 169 252
Eikonal      83
Embedding      129
Equation of heat transfer with absorption (generation)      219
Equation with friction, wave      216
Equation with retarded argument      177
Equation, $\alpha$-regular      215
Equation, Airy      72
Equation, Cauchy — Riemann      218
Equation, convolution      177
Equation, diffusion      345
Equation, eikonal      83
Equation, heat conduction      145
Equation, Helmholtz      146
Equation, Klein — Gordon      144
Equation, klein — gordon hyperbolic      224
Equation, Laplace      145
Equation, petrovskij $\beta$-parabolic      219
Equation, Petrovskij well-defined      215
Equation, Schrodinger      145
Equation, second-order differential      196
Equation, Shilov h-parabolic      218
Equation, transport      53 85
Equation, wave      144
Erdelyi, A.      146 188 199 209 210 251 252
Eskin, G.I. (=ehskin, G.I.)      6 78 114 116 184 217 232 238 251 255
Euler, L.      61 125 182
Example, Friedlander      71
Example, Hadamard      230
Example, Lewy      64
Example, Taylor      74
Fedorova, S.I.      101 117
Fedoryuk, M.V.      54 79 85—87 90 95 96 113 114 116 118
Fedosov, B.V.      24 25 114 116
Fefferman, C.      65 114 115
Formula of eigenvalues, distribution      97
Formula of piecewise smooth functions, differentiation      129
Formula, Atiyah — Bott      108
Formula, D'Alembert      144 237
Formula, differentiation      149
Formula, Dynin — Fedosov      25
Formula, formal      169
Formula, heaviside      129
Formula, Kirchhoff      144 237
Formula, morse      248
Formula, noether-muskhelishvili      25
Formula, Poisson      144 237
Formula, Sokhotskij — Plemelj      155
Formula, translation      150
Fourier integral      149
Fourier, J.B.J.      36 48 56 59 88 125 149 151 153 175 176 213 239
Fredholm, I.      23 24 32 35
Friedlander, F.G.      71 116
Friedrichs, K.      6 114 116
Fubini, G.G.      150 153
Function, Dirac's delta      129
Fundamental solution of boundary-value problem      234
Fundamental solution of differential operator      142
Fundamental solution, advanced      144
Fundamental solution, formal      200
Fundamental solution, invariant      197
Fundamental solution, invariant equation      142
Fundamental solution, retarded      144
Gabriehlov, A.M.      245 250 252
Garding, L.      125 127 182 183 215 229 231 236 240 242—250 252 253
Gel'fand, I.M.      25 125—127 129 134—136 140 143 148 150 152 158 159 167 172 189 191 192 229 234 237 250—253
Generalized function      128
Generalized function, derivative      129
Generalized function, order      135
Generalized function, product      137
Generalized function, temperately growing      161
Generating function of canonical transformation      55
Generating function of lagrangian manifold      93
Generating function, projective      247
Gevrey, M.      48
Giraud, G.      36
Givental, A.B.      114
Glancing surface      73
Glazman, I.M.      96 98 116
Gokhberg, I.Ts.      29 117
Gordon, W.      127 144 186 194 206 216 224
Gorin, E.A.      168 169 251 253
Green, G.      125
Grubb, G.      107 114 117
Grushin, V.V.      146 149 171 212 251 253
Guillemin, V.      44 79 96 112 114 116 117
Gunning, R.      159 251 253
Gureev, T.V.      101 117
Gusejn-zade, S.M.      82 114 115 248—250 252
Hadamard, J.      13 125 127 199 206 230 250 253
Hahn, K.      164 165
Hamilton, W.R.      48 55 84 90 91 92 95
Hamiltonian system      181
Hankel, H.      146 209
Hartogs, F.      247
Heaviside, O.      125 126 129 144
Helmholtz, H.      146 167 168 170 171 184 207 209 210 218 227
Herglotz, G.      125 246
Hersh, R.      66 67 117
Hilbert, D.      13 18 36 96 100 115
Hill, G.W.      113
Holder, O.L.      19 36
Holmgren, E.      39
Hormander staircase      166
Hormander, L.      6 8 9 13 14 17 19 32 35 37 39—42 44—48 58 61 63—65 74 79 85 96 112—114 116 117 125 130 143 145 146 150 154—156 159—161 166—170 181—184 212 214 215 217 222 223 230 250 251 253
Huygens, Ch.      44
Ikawa, M.      117
Ikehara, S.      109
Index, Maslov      94
Index, operator      24
Ivrii, V.Ya. (=ivrij, V.Ya.)      96 100 101 113 114 117
Jacobi, K.G.J.      90—92 95
John, F.      36 37 115
Jordan, C.      39 40
Kajitani, K.      117
Kirchhoff, G.R.      125 144 237
Klein, F.      127 144 171 186 194 206 216 224
Kohn, J.J.      6 113 117
Komech, A.I.      161 253
Korn, A.      36
Kostyuchenko, A.G.      26
Kotake, T.      182 183 250 253
Kramers, H.      78
Kreiss, H.O.      67 117
Krejn, M.G.      29 117
Krejn, S.G. (=krein, S.G.)      127 253
Kronecker, L.      133 234
Kumano-go, H.      6 9 14 17 19 32 35 114 117
Lacuna      244
Lacuna, local      244
Lacuna, strong      244
Laplace, P.S.      40 125 145 175 176 184 200 218 225 227 230 231
Lax, P.      70 86 87 116 118
Lebesgue, H.L.      99 103
Leibniz, G.W.      14
Lemma, Glazman      98
Lemma, Morse      80
Lemma, Weyl      184
Leray, J.      96 113 114 118 125 127 182 183 199 206 246 250 253
Levendorskij, S.Z.      105 118
Levi, E.E.      110
Levitan, B.M.      110 112 118 126
Lewy, H.      64
Lichtenstein, L.      36
Liouville, J.      93
Locally equivalent phase functions      58
Lojasiewicz inequality      169
Lojasiewicz, S.      143 167 169 170 250 254
Lopatinskij determinant      69
Lopatinskij matrix      69
Lopatinskij, Ya.B.      69 222 232 233 254
Lorentz, H.A.      134 186 193 204
Malgrange, B.      125 143 164 254
Manifold, Lagrangian      57 91
Manifold, quantized Lagrangian      94
Manifold, symplectic      54
Map, proper      14
Maslov, V.P.      85—87 90 94—96 113 114 118
Melrose, R.      73 114 118
Merzon, A.      161 165 174 251 254
Method, Maslov canonical operator      90
Method, Riesz complex powers      172
Method, stationary phase      79
Method, subtraction      169
Microlocal analysis      4 113 114
Mikhlin, S.G.      36 113 118 251 254
Mishchenko, A.S.      96 113 114 118
Mizohata, S.      36 38 118
Morse, H.M.      80 81 247 248
Muskhelishvili, N.I.      25
Nazajkinskij, V.E.      96 113 114 118
Neumann problem      225
Nirenberg, L.      6 40 70 71 113 114 117 118
Noether, F.      25
Nuij, W.      242 254
Oblique derivative problem      225
Olejnik, O.A.      114 118
Operator on manifold pseudodifferential pseudodifferential      19
Operator solvable at a point, pseudodifferential      63
Operator with constant coefficients, differential      241
Operator, $\alpha$-regular      215
Operator, $\zeta$ wave      171
Operator, canonical      94
Operator, Cauchy — Riemann      184
Operator, differential      6
Operator, elliptic      183
Operator, elliptic Fourier integral      56
Operator, elliptic pseudodifferential      15
Operator, formal adjoint      9
Operator, Fourier integral      48
Operator, function of      106
Operator, garding hyperbolic      215
Operator, global Fourier integral      60
Operator, Helmholtz      167
Operator, Hill      113
Operator, hyperbolic      243
Operator, hypoelliptic      184
Operator, Klein — Gordon      171
Operator, Laplace      184
Operator, Maslov canonical      94
Operator, multidimensional singular integral      13
Operator, on smooth curve, singular integral      22
Operator, one-dimensional singular integral      12
Operator, Petrovskij hyperbolic      242
Operator, petrovskij strictly hyperbolic      180 215
Operator, petrovskij well-defined      215
Operator, precanonical      93
Operator, principal type differential      60
Operator, principal type pseudodifferential      61
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