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| Авторизация |
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| John F. — Partial Differential Equations |
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| Предметный указатель |
A priori estimates 167
Adjoint differential operator 80
alternative 194
Amplitude 207
Analytic field 82
Analytic function of one variable 2
Analytic function of several variables 70—73
Analytic function, real 64—70
Approximate solution 137 141
Autonomous 9
Backward difference quotient 7
Baire category argument 239
Banach space 49 118 237
Barrier function 115 116
Beltrami equation 38
Bessel function 135
Biharmonic equation 102
Blow-up 17
Boundary-initial-value problem 42 50 139—143 157 158
Burgers' equation 18 214
Canonical form, first-order system 48 164
Cauchy data 11 33 47 56
Cauchy derivative estimate 71
Cauchy formula 70
Cauchy problem, first-order equation 11 13 14 24—27 30
Cauchy problem, quasi-linear system 56
Cauchy problem, second-order equation 33
Cauchy problem, wave equation 88 135—139
Cauchy sequence 118
Cauchy — Kowalevski Theorem 74—77
Cauchy — Riemann equations 2 72
Caustic 129
Characteristic curves 9 10 11 12 13 21 23 24 34 47 50 61
Characteristic direction 9 10 20
Characteristic element 21 24 30
Characteristic equations 9
Characteristic form 58
Characteristic hypersurface 57 59 60
Characteristic line 4 5
Characteristic matrix 58
Characteristic projection 14 17
Characteristic strip 23—30
Compact support 89
Compactness 110 243
Compactness, weak 202
Compatibility condition 33 43 57
complete 118
Cone property 170
Conical sector 170
Conjugate harmonic 2 102
Connected open set 65 66
Conoid solution 30 31
Conservation law 18
Consistency conditions 141
Convergence of distributions 92
Convergence of multiple series 62
Convergence, strong 199
Convergence, weak 199
Convex set 66
Convex set, strictly 116
Courant — Friedrichs — Lewy test 7 8 230
Cutoff function 100
d'Alembertian 126
Darboux's equation 127
DATA 11
Descent 133—135 189
Difference equation 5
Difference equation, stability 7 174
Difference operator 173
Difference quotient, backward 7
Difference quotient, central 174
Dirac function 90 199
Dirichlet data 140
Dirichlet integral 119 125
Dirichlet norm 120 121
Dirichlet principle 125
Dirichlet problem 95 103 106 111—125 155 190—205
Dirichlet problem, modified, generalized 117 120 121 191 198
distribution 90 199
Distribution, solution 91
Divergence form 17
Divergence theorem 79
Domain of dependence 5 6 7 41 85 130 131 153 181 210
Domain of determinacy 85 88
Duhamel's principle 135 144
Eigenfunctions expansion 44 140
Elastic equilibrium equations 188
Elastic waves equations 3 133 156
Element 23 24 27 29
Elliptic higher-order equations 185—205
Elliptic second-order equation 35 38 60
Elliptic strongly 195 196
Energy identity 95 164
Energy inequality 165 174
Energy integral 139 142
Energy sum 176
Entire function 73 219
Envelope 20 29 30
Error function 211
Euler — Lagrange equations 32
Euler — Poisson — Darboux equation 128
Euler's differential equation 15 16
Finite differences, method of 5 172 227
First-order systems 46—53
First-order systems, canonical form 48
First-order systems, Cauchy problem 47
First-order systems, initial-boundary value problem 50
First-order systems, initial-value problem 47
Focussing effect 129
Fourier reciprocal formula 146
Fourier transform 146
Fredholm alternative 195
frequency 207
Functional, bounded 118
Functional, linear 118
Fundamental solution 91 92 101 102 161 186—190
Garding hyperbolicity condition 149 151 155 157
Garding inequality 194 196 197
Gauss divergence theorem 79
Gauss law of arithmetic mean 99 104
General solution 11 29
Generalized solution 35 41 57 91
Gradient catastrophe 17
Green's function 107 110
Green's identities 94
Gronwall's lemma 172
Hadamard's method of descent 133—135 189
Hamilton — Jacobi equation 31
Harmonic conjugate 2 102
Harmonic function 2 97 98 109
Harnack's inequality 111
Heat (conduction) equation 3 88 206—227
Heat (conduction) equation, initial-value problem 206—215
Heat (conduction) equation, maximum principle 210 215 216
Heat (conduction) equation, mixed problem 220 222
Heat (conduction) equation, non-negative solutions 222—227
Heat (conduction) equation, regularity 211 218—220 222
Heat (conduction) equation, uniqueness 211 216
Hilbert space 118 190 198
Hilbert space, representation theorem 118 125
Hodograph method 40
Holmgren's uniqueness theorem 80—87 144
Homogeneous function, Euler equation 15 16
Huygens' principle 131 134
Huygens' wave front generation 31 130
Hyperbolic 145 155
Hyperbolic constant coefficients 143—163
Hyperbolic first-order systems 48
Hyperbolic Garding condition 149
Hyperbolic second-order equation 35 38
| Hyperbolic strictly 152 160
Hyperbolic symmetric systems 163—184
Hyperplane 119
Ill-posed problem 77 155
Implicit function theorem 69
Influence 41
Initial value 4 11 41 47
Initial-boundary value problem 42 50 139—143 157 158
Initial-value problem 155
Initial-value problem, first-order equation 7 11
Initial-value problem, heat equation 206—215
Initial-value problem, linear parabolic equations 227—234
Initial-value problem, standard 144 156
Initial-value problem, system of first-order equations 47
Initial-value problem, wave equation 41 129 132 135 156 162
Inner product space 117
Instability of difference scheme 6 8
Integral surface 9 10 13 20 21 23 24 28
Irreversible 206
Jump 36 37
Korteweg — de Vries equation 4
Lagrange — Green identity 80
Lame constants 3
Laplace equation 2 78 94—125
Laplace equation, Cauchy problem 98
Laplace equation, compactness 109
Laplace equation, Dirichlet problem 95 103 106 111—125
Laplace equation, fundamental solution 96—98
Laplace equation, inhomogeneous 100
Laplace equation, maximum principle 103—106
Laplace equation, mean value theorem 99 104
Laplace equation, Neumann problem 95 103
Laplace operator 2 94
Lattice 227
Lax — Milgram lemma 194
Legendre transformation 40
Lewy's example 235—239
Line element 24
Linear equation 1
Linear equation, second-order 37—39
Liouville's theorem 110
Lorentz transformation 139
Majorants 67
Majorants, method of 67 75
Maximum principle 101—106 112 210 215 216 229
Maxwell's equations 2 169
Mean value theorem 99 104
Minimal surface equation 3 39
Mixed problem 43 45 50 139—143 157—158 220 222
Monge cone 20 28
Multi-index notation 54
Multiple infinite series 62
Navier — Stokes equations 4
Neumann problem 95 103
Non-characteristic curve 34 35
Non-characteristic hyper-surface 57 59
Norm 117 118
Normal form of second-order equation 38
o.d.e. 9
Order 1
Orthonormal sequence 201
p.d.e. 1
Paley — Wiener theorem 153
Parabolic 35 206—234
Parallel curves 29
Parseval's identity 168
Partition of unity 196
Perron's method 111—116
Plane element 22
Plane waves, decomposition into 161 186
Plane waves, method of 158—163
Poincare inequality 120 125 193
Poisson's differential equation 100 103
Poisson's formula 99 110
Poisson's integral formula 106—108 111
Poisson's kernel 107
Polydisc 70
Polytropic gas 3
potential energy 3
Potential function 2
Potential Newtonian 103
Potential velocity 3
Power series 63—64
Principal part of differentia] operator 57 151
Propagation of disturbances 154
Propagation of elements 24 29
Propagation of singularities 35 37 60
Propagation of waves 5 28
Quasi-linear equation 1 3 14
Quasi-linear system 52 56
Radon problem 162
Radon transform 162
Ray 24 29
Real analytic functions 64—70
Reduced wave equation 101 195
Reflection 141 142 220 236
Rellich's lemma 195
Representation theorem 118 125
Riesz — Schauder 195
Round-off errors 6 8
scalar 117
Schauder's method 182
Schroedinger's wave equation 3
Schwartz notation 54—55
Separable 201
Separation of variables 44
Shift operator 6 173
Shock condition 18
Simple waves 52
Singular solutions 17 18 35 57
Sobolev inequalities 168—170 178
Spacelike 28 138 139 145 155 171
Spherical means 126
Spherical symmetry 95 101 132
Stability of difference scheme 7 173 228 230
Standard form 74 144
Strict derivative 200 201
Strict hyperbolicity 152 160
Strict solution 36
Strip 20
Strip characteristic 23
Strip condition 23 33
Strip support 23
Strong derivative 200 201
Strong ellipticity 195 196
Subharmonic function 99 101 104 112 115
Support compact 89
Support of function 89
Support of strip 23
Support, plane 88
Symbol 58
Symmetric hyperbolic systems 163—184
Telegraph equation 135
Test function 89 199
Theta function 221
Timelike 28
Timelike, Cauchy problem 88 139
Transition conditions 35
Tricomi equation 38
Tychonoff solutions 211 217
TYPE 35
Unique continuation of analytic functions 70
Unique continuation of real analytic functions 65
Unit sphere area 96
Vector space 117
Velocity potential 3
Vibrating string 40
Water waves 4 132
Wave equation 2
Wave equation, 1 dimension 40—45
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