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| Авторизация |
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| Jeffrey A., Taniuti T. — Mathematics in Science and Engineering: volume 9. Non-linear wave propagation |
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| Предметный указатель |
 erenkov radiation 53 60
 th Riemann invariant 87 88
th simple wave 87 88
Acoustics, geometrical 159 ff
Adiabatic, curve 329
Adiabatic, gas 58
Adiabatic, law for water waves 64
Adiabatic, reversible fluid 170
Alfven 6
Alfven, number 244 295
Alfven, rays 185 186 193 201
Alfven, shock  264
Alfven, shock and slow shock 268 269 270
Alfven, speed 173
Alfven, wave 176 200 261
Alfven, wave in incompressible fluid 175 200
Alfven, waves, outgoing 222 346
Aligned-field flow 293 354
Analytic initial data 10 13 27 40
Axis, optical 56
Basis 325
Bernoulli’s equation 300 354
Bernoulli’s theorem 294 300
Bilinear form 323
Biorthogonal set 325
Body force, Lorentz 168
Boundary conditions on piston 260 ff
Boundary conditions on spacelike arc 99 100
Bounded derivative and Lipschitz continuity 27
Branches of a shock 229 231 311 336
Cauchy, problem 13 40
Cauchy, sequence 20
Cavitation in pure gas wave 269
Cavitation in slow rarefaction 209 210 260 262 266 271
Centred rarefaction wave 134 345
Centred rarefaction wave, fast 264
Centred rarefaction wave, slow 262
Centred simple wave 73 91
Characteristic equations 7 12 35 38
Characteristic equations for a transmission line 83
Characteristic equations for gas dynamics 59
Characteristic equations for general non-linear equation 14
Characteristic equations for magnetohydrodynamics 172
Characteristic equations for non-isentropic flow 59
Characteristic equations for shallow water 81
Characteristic equations for supersonic flow 79
Characteristics as wavefront 28
Characteristics,  67 ff 79 81 300
Characteristics, bounding constant state 88
Characteristics, curves 7 12 66 89 142
Characteristics, curvilinear coordinate net 199
Characteristics, determinant 34 324
Characteristics, direction 14 36 143
Characteristics, field 89 98 68 70 72 79 304 307
Characteristics, hypercone 46 52
Characteristics, manifold 34 65
Characteristics, parametisation 67 68
Characteristics, rays 184
Characteristics, surface 36
Charge conservation law 48
Collision of shocks 141 292
Completely exceptional system 90 106 108
Compressible flow 92
Compression, fast and slow waves 209
Compression, maximum 210 229 242 270
Compressive shock 328
Condition, (C) 227 333
Condition, (R) 227
Confinement of plasma 319
Conformability of matrices 321 ff
Conical refraction 194
Conservation laws 57 111
Conservation laws, differential form 112
Conservation laws, energy 57 169 217
Conservation laws, generalised 116
Conservation laws, generalised, integral form 111
Conservation laws, generalised, magnetohydrodynamic 214 ff
Conservation laws, generalised, mass, momentum and energy 57
Conservation laws, generalised, symmetric hyperbolic 152
Conservation of magnetic flux 225
Constant state line 87
Constitutive equations 49 167
Contact, discontinuity 136 160 218 249 252 255
Contact, layer 213
Contact, surface 60 109 176 289 338
Contact, transformation 347 ff
Continuity, equation 169
Continuity, Lipschitz 27 39 100 103
Contraction mapping 20 21 99
Convergence in the mean 121
Convergence, strong 121 123
Convergence, weak 121
Courant, method of 142 ff
Critical, point 106 109
Critical, speed 304 307
Critical, time  100 104 107
Crystal optics 53 185
Cusp 72
Derivative, directional 10 33 66 81 146
Derivative, generalised 118
Determinant, characteristic 34 324
Determined system 29
Diadic product 58
Diagonalising matrix 96
Difference quotients, forward and backward 143
Differentiation of a matrix 322 323
Differentiation, along a ray 154
Directions, characteristic 14 36 143
Discontinuity, development and propagation of 90 100
Discontinuity, exceptional 128 129 134 250 345
Discontinuity, propagation of weak 149 ff
Discontinuity, spatial 47 52 61 186 293
Discontinuity, static case 317 ff
Discontinuity, weak 260
Displacement vector, electric 168
Divergence condition, variational 191
Domain of dependence 9 15 99 142 144
Domain of dependence, existence and uniqueness 21 24
Double layer shock 258
Eigenvalues of a matrix 324
Eigenvalues redundant 38
Eigenvalues, multiplicity k 326
Eigenvectors of a matrix 324
Eigenvectors, generalised left and right 326
Eigenvectors, jth right 325
Eigenvectors, left 66 75 325
Eigenvectors, right 87 92 325
Electromagnetic, field equations in a conductor 168
Electromagnetic, polarised waves 55
Electromagnetic, scalar potential 50
Electromagnetic, transverse nature of waves 49
Electromagnetic, vector potential 50 196
Elliptic equation 6
Elliptic-hyperbolic, magnetohydrodynamic flow 187 311
Energy, internal 58 169
Energy, total 57 169
Entropy wave, degenerate 177
Entropy, condition 115 122
Entropy, disturbance, matrix representation 341
Entropy, increase across shock 328
Entropy, jump in fast shock 230
Entropy, jump in slow shock 239
Entropy, simple wave 203
Envelope, of discontinuities 72
Equation, of mixed type 6
Equi-pressure surfaces 318 319
Evolutionary condition 125 ff
Evolutionary condition and fast shocks 231
Evolutionary condition and gas shocks 137 ff
Evolutionary condition and slow shocks 234 ff
| Evolutionary condition in magnetohydrodynamics 218 220 256 345
Evolutionary, discontinuities 128
Evolutionary, weakly 258
Exceptional 345
Exceptional case 100 107 110 213
Exceptional system 90 106
Expansion ratio 156 158
Expansion ratio in magnetohydrodynamics 194
Expansion wave 73
Expansion wave and initial discontinuity 74
Fast disturbance, matrix representation 340
Fast shock 217 218 219 224 227 259 264 269 313 335
Fast shock and Alfven shock 220
Fast shock,  limit 247 ff
Fast shock, dependence on parameters 232 233
Fast shock, type (1) 229 240 335
Fast shock, type (2) 229 241 335
Fast wave 173 183 184 205 208 295 304
Fast wave, simple 203 210 212
Field, divergence free 112
Field, divergence free, kth 89
Finite difference equations 143
Finite difference equations, along characteristics 146
Finite discontinuity, propagation 90 ff
First order quasi-linear systems 24 ff
First order quasi-linear systems and Cauchy problem 40
Fixed point theorem 21
Flow, aligned-field 354
Flow, homentropic 299
Flow, incompressible magnetohydrodynamic 198
Flow, isentropic 71 91
Flow, isentropic and irrotational plane 354
Flow, non-isentropic 58 92
Flow, past a conducting convex wall 309
Flow, past a sharp corner 297 312
Flow, steady supersonic 76
Fluid motion equations 169
Fluid pressure 176
Flux, magnetic 225
Flux, scalar 111
Free surface 62
Fresnel equation 54
Friedrichs diagram 181 ff 186
Frozen-in condition 197 198 210
Functional, linear 117
Gas, basic physical properties 220 327
Gas, dynamic conservation laws 135
Gas, shock 136 244 258 265 334
Gas, simple waves 334
Gaussian units 167
Genuinely non-linear 91 121
Goursat problem 17
Hamilton — Jacobi equation 42 184
Hamiltonian 42 46 184 193
Heat, conduction coefficient 58
Heat, equation 58
Heat, flow vector 169
Hodograph, plane 303 352
Hodograph, transformation 80 299 302 352
Homentropic flow 299
Homogeneous hyperbolic equations 66 79
Hugoniot function 217 327
Hydrodynamic contact discontinuity 138
Hydrodynamics, basic equations 57
Hydromagnetic, equations in matrix form 339 ff
Hydromagnetic, shock relations 334 ff
Hydromagnetic, simple waves 337
Hydromagnetic, stability 320
Hydrostatic pressure 63
Hyperbolic equations 6 37 66
Hyperbolic equations, normal form 7 17 19
Hyperbolic equations, symmetric 153
Hyperbolic, totally 37 38 94
Hyperbolic, ultra 37 38
Hyperbolic-fast 315 ff
Hyperbolic-slow 315 ff
Hyperplane 33
Identity matrix 322
Incompressible, fluid 61
Incompressible, magnetohydrodynamic flow 198
Indefinite quadratic form 324
Indeterminacy of normal derivative 34
Initial, curve 16
Initial, data 9
Initial, interval and boundary values 98
Initial, point 208
Initial, value problem 24
Integral, curves for magnetohydrodynamic flow 205 206
Integral, equation, solution by iteration 21
Intermediate discontinuity 129
Intersection of characteristics 70 72 103
Invariant, measure 196
Invariant, transformation 218
Inverse matrix 322
Involutory transformation 349
Isentropic, flow 71 91 105 294 354
Isentropic, spherical flow 108
Jacobian 67 101 352
Jacobi’s theorem 155
Joule heating 244
Jump conditions and evolutionary condition 226
Jump conditions, across wavefront 4 5 102 107
Jump in variational quantities 151
Jump, discontinuity 113
Klein bottle 319
Kronecker delta 46
Lax’s condition 125 128
Lax’s condition and gas shock 138
Left eigenvector 66 75 325
Legendre transform 311 349 351
Legendre transform and potential flow 352
Limit,  fast shock 240
Limit, slow shock 247
Limit, fast shock 247
Limit, slow shock 247
Limit, shocks 238 ff 258
Limit, strong 121 123
Limit, weak 121
Limiting operation in  102
Linear equations 3 29 32
Linearly independent eigenvectors 325
Lipschitz continuity 27 39 100 103
Lorentz, body force 168
Lorentz, transformation 51
Lundquist equations 171
Lundquist equations and steady spatial discontinuities 317 ff
Lundquist equations, isentropic flow 189
Lundquist equations, linearised one-dimensional 221 342
Mach, angle 78
Mach, fast and slow wave 295 297 302 305 307
Mach, lines 77
Mach, number 77 295
Mach, wave 60 186 293 297
Magnetic, lines of force and properties 195 ff
Magnetic, pressure 176 204 210 297 319
Magnetic, Riemann invariant 207
Magnetic, stress tensor 169
Magnetic, surfaces 318
Magnetoacoustic waves 174 222 223 345
Magnetoacoustic waves and Alfven shocks 281
Magnetoacoustic waves, combination and interaction 280 ff
Magnetoacoustic waves, shock 261 345
Magnetoacoustic waves, simple 203 204
Magnetohydrodynamic, basic assumptions 167
Magnetohydrodynamic, characteristic equations 172
Magnetohydrodynamic, conservation laws 214 ff
Magnetohydrodynamic, elliptic-hyperbolic flow 187 311
Magnetohydrodynamic, evolutionary conditions 218 220 256 345
Magnetohydrodynamic, incompressible flow 198
Magnetohydrodynamic, mechanical relations 216 219 226
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