Egorov Yu.V. (Ed), Shubin M.A. (Ed) — Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients :: Электронная библиотека попечительского совета мехмата МГУ

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Egorov Yu.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 Yu.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:

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

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Предметный указатель

Amplitude of Fourier integral operater      49
Amplitude of pseudodifferential operater      9
Amplitude, classical      11
Bicharacteristic(s), glancing      73
Bicharacteristic(s), null      74
Big singularity      112
Boundary value of analytic function      141
Boundary-value problem, regular      221 226
Boundary-value problem, well-posed      231
Cauchy problem      225
Caustics      90
Characteristic cone      179 183 242
Characteristic cone, conoid      183
Characteristic cone, conormal      178
Characteristic cone, equation      178
Characteristic cone, hypersurface      179
Characteristic cone, plane      179
Characteristic cone, polynomial      241
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
Conical subset      45
Conjecture, Sato      73
Convolution      108
Convolution of functions      137
Convolution of functions generalized functions      137
Differential form, closed      54
Differential form, non-degenerate      54
Differential operator      6
Differential operator, elliptic      15
Differential operator, operator      102
Diffractive      74
Diffractive of contact      74
Diffractive, critical      79
Diffractive, elliptic boundary      74
Diffractive, focal      82
Diffractive, glancing      74
Diffractive, higher order      74
Diffractive, hyperbolic      74
Diffractive, non-degenerate      74
Diffractive, periodic flow      111
Diffractive, stationary phase      79
Direction, hyperbolic      71
Dirichlet problem      224
Dirichlet problem for operator      229
distribution      128
Distribution with compact support      135
Distribution, exponentially growing      161
Distribution, Fourier      59
Distribution, temperately growing      141
Division problem      164
Division problem in classes of tempered distributions      167
Eikonal      83
Embedding      129
Equation with friction, wave      216
Equation with retarded argument      177
Equation, Airy      72
Equation, Cauchy — Riemann      218
Equation, convolution      177
Equation, diffusion      145
Equation, eikonal      83
Equation, heat conduction      145
Equation, Helmholtz      146
Equation, hyperbolic      224
Equation, hyperbolic of heat transfer with absorption (generation)      219
Equation, Klein — Gordon      144
Equation, Laplace      145
Equation, Petrovskij well-defined      215
Equation, Petrovskij well-defined, $\beta$ -regular      215
Equation, Schroedinger      145
Equation, second-order differential      196
Equation, Shilov h-parabolic      218
Equation, transport      53 85
Equation, wave      144
Example, Friedlander      71
Example, Hadamard      230
Example, Lewy      64
Example, Taylor      74
Formula, Atiyah — Bott      108
Formula, differentiation      149
Formula, Dynin — Fedosov      25
Formula, d’Alembert      144 237
Formula, Kirchhoff      144 237
Formula, Noether — Muskhelishvili      25
Formula, Poisson      144 237
Formula, Sokhotskij — Plemelj      155
Formula, translation      150
Fourier integral      149
Function of eigenvalues, distribution      97
Function, Dirac’s delta      129
Function, formal      169
Function, Heaviside      129
Function, Morse      248
Fundamental solution, advanced      144
Fundamental solution, advanced of boundary-value problem      234
Fundamental solution, advanced, formal      200
Fundamental solution, advanced, invariant      197
Fundamental solution, advanced, invariant equation      142
Fundamental solution, differential operator      142
Fundamental solution, retarded      144
Generalized function      128
Generalized function, derivative      129
Generalized function, order      135
Generalized function, product      137
Generalized function, temperately growing      161
Generating function of canonical, Lagrangian manifold      93
Generating function of canonical, projective      247
Generating function of canonical, transformation      55
Glancing surface      73
Gliding      74
Hamiltonian system      181
Hoermander staircase      166
Index, Maslov      94
Index, operator      24
Lacuna      244
Lacuna, local      244
Lacuna, strong      244
Lemma, Glazman      98
Lemma, Morse      80
Lemma, Weyl      184

Light      203
Light, past light      203
Locally equivalent phase functions      58
Lojasiewicz inequality      169
Lopatinskij determinant      69
Lopatinskij determinant, matrix      69
Manifold, Lagrangian      57 91
Manifold, quantized Lagrangian      94
Manifold, symplectic      54
Map, proper      14
Method, Maslov canonical operator      90
Method, Riesz complex powers      172
Method, stationary phase      79
Method, subtraction      169
Microlocal analysis      4 113 114
Neumann problem      225
Oblique derivative problem      225
Operator, $\alpha$ -regular      215
Operator, $\zeta$ -function of      106
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, Girding 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      13
Operator, n manifold      19
Operator, olvable at a point      63
Operator, on smooth curve      22
Operator, one-dimensional      12
Operator, Petrovskij hyperbolic      242
Operator, precanonical      93
Operator, principal type      61
Operator, principal type differential      60
Operator, properly supported      14
Operator, pseudodifferential      7
Operator, semi-globally solvable      63
Operator, singular integral      36
Operator, spectral function      108
Operator, Stein extension      238
Operator, strictly      180 215
Operator, strictly elliptic      167
Operator, subelliptic      65
Operator, transpose      8
Operator, uniformly elliptic      32
Operator, wave      171
Operator, well-defined      215
Parametrix      16
Parseval identity      151
Parseval identity, theorem      152
Petrovskij class      244
Petrovskij class, criterion      244
Petrovskij class, cycle      247
Petrovskij class, local      244
Phase function      49
Phase function, Lagrangian manifold      58
Phase function, local      58
Phase function, non-degenerate      57
Point, absolutely periodic      112
Poisson bracket      55
Poisson bracket, kernel      235
Poisson bracket, relation      111
Polyhomogeneous      11
Potential, advanced      144
Potential, retarded      144
Principal      11
Principal homogeneous part of operator      178
Principal homogeneous part of operator value of integral      13
Principle, Courant’s minimax      97
Quantization      34
Quantization, Weyl      34
Ray      82
Regularization problem      168
Regularization problem, formal function      169
Relation, homogeneous canonical      60
Root, $\alpha$ -well-posed      214
Root, Petrovskij well-defined      214
Root, stable      214
Root, unstable      214
Set, asymptotically time-like      138
Solution, asymptotic      83
Solution, asymptotic, rapidly oscillating      83
Space, Schwartz      141
Space, Schwartz, test functions      128
Space-like      138
Structure, Symplectic      54
Support of function      134
Support of function generalized      134
Support of function generalized, singular      136
Swallow-tail      248
Symbol, classical      11
symmetric      34
Symmetric Weyl      33
Theorem, Calderon      39
Theorem, Calderon — Zygmund      36
Theorem, composition      15
Theorem, Ikehara      109
Theorem, mean value      148
Theorem, Payley — Wiener      150
Theorem, regularity      17
Transformation, canonical      54
Transformation, canonical, contact      213
Transformation, canonical, Fourier      149
Transformation, canonical, Fourier — Laplace      175
Transformation, canonical, Hilbert      13
Transformation, canonical, Laplace      176
Transformation, canonical, Lorentz      134
Wave diffusion      147 203
Wave diffusion front      82 180
Wave diffusion front set      44 48
Wave diffusion of generalized function      180
Wave diffusion, operator      243
Weak convergence      128
Weyl symbol      33
Weyl symbol, h-symbol      34

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