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John F. — Partial Differential Equations
John F. — Partial  Differential Equations

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Название: Partial Differential Equations

Автор: John F.

Аннотация:

Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Fourth Edition

Год издания: 1982

Количество страниц: 249

Добавлена в каталог: 08.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
1 2
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