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| Noble B. — Methods based on the Wiener-Hopf technique for the solution of PDEs |
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| Предметный указатель |
Abelian theorems 36 46 57
Absorbent boundaries (see Resistive boundaries)
Aerofoil, quarter-infinite 95
Aerofoil, two-dimensional 173
Alblas, J. B. 96 236
Ament, W. J. 47
Analytic continuation 7ff 38ff
Antenna, biconical 218
Antenna, cylindrical rod 213
Approximate factorization 160ff
Approximate methods 178ff 236 generalized)
Approximate methods for integral equations 23ff 233ff
Approximate methods for strips and slits 203ff
Approximate methods for thick plates 187ff
Approximate methods, meaning of “approximate” 180
Approximate methods, miscellaneous formulations 181ff
Asymptotic expansions for contour integrals 33ff 46
Asymptotic expansions for transforms 36
Asymptotic expansions in approximate solutions 200ff (see also Far-field)
Baiun, L. L. 122
Baker, B. B. and Copson, E. T. 70 206
Baldwin, G. L. and Heins, A. E. 125
Bazer, J. and Karp, S. N. 73 128 153 166 167
Biharmonic equation (see also Elastic medium)
Biharmonic equation, approximate factorization for 162
Biharmonic equation, stresses in strip 138
Boundary conditions, specified by arbitrary functions 7 7ff
Boundary layer on flat plate 96 97
Bouwkamp, C. J. 75 179 218
Branch Cuts 8ff
Branch cuts, special cases 9 19 38 39
Branch points and poles (see Poles and branch points)
Carlson, J. F. and Heins, A. E. 103 133
Carrier, G. F. and Munk, W. H. 94
Carslaw, H. S. 72
Chester, W. 20 132
Churchill, R. V. 27
Circular waveguide (see Duct cylindrical)
Clemmow, P. C. 36 88 93 94 152
Cone, Laplace’s equation 165
Cone, wave equation 218
Contour integrals for sum and product decompositions 18ff
Contour integrals special type 31ff.
Convection of heat from flat plate 94
Conventions x 10 28 86
Copson, E. T. vii 5 6 70 95 231
Copson’s method 231
Cosine transform 147 212
Cylindrical pipe (see Duct cylindrical)
Davison, B. 168
Dielectric slab 211 213
Diffraction (see Disc Duct Halfplanes Strips
Diffraction, methods other than the Wiener-Hopf for 125 179
Dirac delta function 43
Disc, Laplace’s equation 166 231
Disc, low frequency 213ff 231
Disc, wave equation, high frequency 219
Divergent integrals 64
Doetsch, G. 27 36
Dual integral equations for boundary conditions specified arbitrarily 77ff
Dual integral equations for three-part problems 231
Dual integral equations formulation in terms of 4 58 150
Dual integral equations general comments 48 77 221 236
Dual integral equations, exact solution of general cases 77ff 222ff
Dual integral equations, half-plane problem solved by 58ff
Dual integral equations, involving Bessel functions viii 221
Dual integral equations, multiplying factor method for 58ff 77ff 222ff
Dual integral equations, reduction to complex variable equation 150 151 221
Duct, cylindrical, finite length 207
Duct, infinite length, resistive wall 134
Duct, propagated and attenuated modes 110
Duct, radiation from 11
Duct, radiation from coaxial 133 154
Duct, semi-infinite tube in 121
Duct, semi-infinite, electromagnetic waves 132
Duct, two-dimensional, finite length 207
Duct, two-dimensional, infinite length with semi-infinite obstacle, dielectric slab 211
Duct, two-dimensional, infinite length with step 196 207ff
Duct, two-dimensional, infinite length with strip across 122ff 212
Duct, two-dimensional, propagated and attenuated modes 98ff
Duct, two-dimensional, resistive wall 133
Duct, two-dimensional, semi-infinite (see Half-planes two
Duct, two-dimensional, set of posts 174
Duct, two-dimensional, solution via simultaneous linear algebraic equations 175
Duct, two-dimensional, strip of finite thickness parallel to wall 212
Duct, two-dimensional, strip parallel to wall 118ff
Duct, wave incident on 116ff
Edge conditions 51 74ff
Edge conditions, references 75
Elastic medium (see also Biharmonic equation)
Elastic medium, diffraction by half-plane in 96
Elastic medium, stresses in wedge with mixed boundary condition 173
Electromagnetic waves, boundary conditions 134
Electromagnetic waves, diffraction by half-plane 95
Electromagnetic waves, diffraction by semi-infinite cylinder 132
Electromagnetic waves, edge conditions 76
Electromagnetic waves, terminology 85 92
End correction, cylindrical tube 115
End correction, thick semi-infinite strip 196
Erdelyi, A. 36 46
Erdelyi, A. et al. 148 176 213
Factorization (see Product factorization)
Far-field, examples of calculation of 105 110 115 192 206
Fel’d, A. N. 174
Fock, V. 168
Fourier transforms 2
Fourier transforms, basic example 53ff
Fox, E. N. 232
Fox’s integral identity 232
Fredholm integral equations, first kind (see Wiener-Hopf integral equations)
Fredholm integral equations, second kind 221
Fresnel functions 33 45 73 213
Function-theoretic methods 153
Gamma functions 40
Gamma functions, factorization by means of 41 167 171 215
Greene, T. R. and Heins, A. E. 94
Green’s function 6
Half-planes with flange 183
Half-planes, algebraic equations 175
Half-planes, dielectric material 213
Half-planes, infinite set of staggered 133
Half-planes, single infinitely thin, basic (Sommerfeld) diffraction problem 48ff
Half-planes, single infinitely thin, diffraction of electromagnetic waves by 95
Half-planes, single infinitely thin, finite resistivity 83
Half-planes, single infinitely thin, generalizations of basic problem 5
Half-planes, single of finite thickness 181 187ff
Half-planes, three parallel 154
Half-planes, two parallel, radiation from 105ff
Half-planes, two parallel, staggered 154
Half-planes, wave falling on 100ff 125 126
Hankel functions, asymptotic behaviour 45
Hankel functions, integral representation 32
Harrington, R. F. 88
Heins, A. E. 94 103 127 131 133 134 157 171
Heins, A. E. and Carlson, J. F. 133
Heins, A. E. and Feshbach, H. 92 93 134
Hilbert problem 49 14
Hilbert problem, equation application 169
Hopf, E. 168
Imperfect conductivity (see Resistive boundaries)
Indentation of contour 30 44 86
Indentation of contour for transform in time 44
Infinite product 15 40 103 129 130
Infinite product or gamma functions 41
Infinite product, asymptotic behaviour of 104 128 129
Infinite product, computation of 127 128
Institute of Mathematical Sciences, New York, reports 237
Integral equation method, general remarks 49 71 76 236
Integral equations (see Fredholm Volterra Wiener-Hopf)
Integral functions 6 178 197
| Jets 139
Jones, D. S. vii, viii 48 52 75 95 97 127 130 131 167 173 187 190 195 196 199 200 207 231
Jones’s method for approximate solutions 17 8ff 236
Jones’s method for boundary conditions specified arbitrarily 79ff
Jones’s method, detailed application to a special example 52ff
Jones’s method, general remarks 48 71 76 98
Jones’s method, routine applications 100ff
Jost, Res 219
Karp, S. N. and Russek, A. 206
Karp, S. N. and Williams, W. E. 125
Klunker, E. B. and Harder, K. C. 139
Koiter, W. T. 75 139 161 162 173
Kourganoff, V. 133 168
Laplace transform 10 21 52 86
Laplace transform, complete equivalence with Fourier transform 22 26
Laplace-type equations 135 (see also Biharmonic equation)
Laplace’s equation as limit of wave equation 135ff
Laplace’s equation in jet problem 140
Laplace’s equation in polar coordinates 164ff 177
Latter, R. 236
Lebedev — Kontorovich transform 148 213ff
Lebesgue integration, reason for not using 23
Leitner, A. and WELLS,C.P. 213 216
Lennox, S. C. 139
Levine, H. 236 242
Levine, H. and Sch winger, J. 20 42 115 130 132
Levine, H. and Wu, T. T. 236
Lewin, L. 131 179 242
Lewis, J. A. and Carrier, G. F. 97
Linfoot, E. H. and Shepherd, W. M. 175
Liouville’s theorem 6 38 57 69 103 114
Magnus, W. 175
Magnus, W. and Oberhettinger, F. 175
Marcuvitz, N. 122 133 179
Mark, C. 168
Marshak, R. E. 168
Maue, A. W. 75 96
Meier, J. A. and Leitner, A. 218
Meixner, J. 75
Meromorphic functions 39
Miles, J. W. 95
Milne’s integral equation 167
Milne’s integral, equation 167
Milne’s integral, reduction of more general types to Fredholm equations of second kind 232 233ff
Milne’s integral, reduction to repeated Volterra equations 230
Milne’s integral, solution by the Wiener — Hopf technique 67ff 167ff 227
Mixed boundary value problem 1
Mixed boundary value problem, solution of a specific example 77ff
Mixed boundary value problem, three-part 183 203ff 231ff
Mixed boundary value problem, two-part, general theory 147
Morse, P. M. and Fesiibaoh, H. 02 115 131 134 179
Multiplying factor method 58ff 78ff 22
Muskhelishvili, N. I. 142 144 146 158
Notation 54
Notation in certain approximate methods 182 197
Numerical evaluation of infinite, products 127 128
Numerical tables viii 122 131
Oberhettinger, F. 36
Oseen’s equations 97
Pack, D. C. viii 139
Pai, S. I. 139
Papadopoulos, V. M. 134 196
Pearson, J. D. 132
Perpendicular boundaries 178 181 187ff 207ff
Placzek, G. 168
Placzek, G. and Seidel, W. 168
Plemelj formulae 47 145
Pol, B. van dee and Bremmer, H. 27 36
Polar coordinates, Laplace’s equation 164ff 177
Polar coordinates, steady-state wave equation 148 214ff
Polar coordinates, wedge of elastic material 173
Poles and branch points 47 133 207
Product factorization 14ff
Product factorization, approximate 160ff
Product factorization, general theorems 15 41
Product factorization, involving gamma functions 41 167 171 215
Quantum mechanics, reference to problem in 219
Quarter-plane aerofoil 95
Radiation condition at infinity 2 31
Radiation-type boundary conditions (see Resistive boundaries)
Radio-wave propagation over landsea interface 93 94
Reflection coefficient in duct 110 114 120 124
Regularity, of functions defined by integrals 1
Resistive boundaries, half-plane 83ff
Resistive boundaries, notation 134
Resistive boundaries, strip across duct 212
Resistive boundaries, strip parallel to walls of duct 120
Rod, solid cylindrical, finite length 213
Rod, solid cylindrical, semi-infinite 196
Scattering cross-section of disc 218
Schwinger, J. vii
Semi-infinite plane (see Half-planes)
Senior, T. B. A. 83 85 92 93 134
Separation of variables 1 147 149
Simultaneous linear algebraic equations from simultaneous Wiener-Hopf equations 155
Simultaneous linear algebraic equations in approximate solutions 185 190ff 208 217
Simultaneous linear algebraic equations in duct problem 175
Simultaneous linear algebraic equations in half-plane problem 176
Simultaneous linear algebraic equations, solution of special sets 173 174ff
Simultaneous Wiener-Hopf equations in electromagnetic cylindrical duct problem 132
Simultaneous Wiener-Hopf equations in electromagnetic half-plane problem 95
Simultaneous Wiener-Hopf equations in two-dimensional duct problems 121 154
Simultaneous Wiener-Hopf equations, general theory 153ff
Slits (see Strips and slits)
Sneddon, I. N. viii 2 96 168 231 236
Sommerfeld, half-plane problem 48ff
Sommerfeld, radiation condition 31
Sound waves (see Duct Half-planes etc.)
Source distribution 44 52 87
Sparenberg, J. A. 169 171
Steady-state wave equation 28
Steepest descent 34
Strips and slits of finite thickness and finite length 213
Strips and slits of finite thickness, induct 212
Strips and slits of finite thickness, semi-infinite length 181 187ff
Strips and slits of finite width, Laplace’s equation 177
Strips and slits of finite width, low frequency 218
Strips and slits of finite width, wave equation, high frequency 183 203ff 219
Sum decomposition in approximate solutions 179 186
Sum decomposition, applications of 80 179 186 198 228
Sum decomposition, function with poles 39
Sum decomposition, general formulae for concrete cases 18
Sum decomposition, general theorem 13
Superposition, method of 81 87
Tables (see Numerical tables)
Tides in permeable rock 94
Titchmarsh, E. C. 2 5 8 11 39 40 41 42 168 171
Titchmarsh’s method 171
Titchmarsh’s method in wedge problems 219
Titchmarsh’s method or evaluation of integrals 33
Titchmarsh’s method or sum decompositions 47
Titchmarsh’s method, applied to diffraction by half-plane 176
Transient problems 28 97
Tranter, C. J. 2
Uniqueness 72
Uniqueness and edge conditions 51 74
Uniqueness, equations 69 168
Vajnshtejn, L. A. 20 115 125 130 131 132 153
Vajnshtejn-Karp-Clemmow method 49 153 213
Verification of solution 72
via the Hilbert, problem 169
via the Hilbert, special equations 171 177
via the Hilbert, uniqueness of solution 69 168
Viscous medium 96 97 139
Volterra integral equations 229 230 233
Water waves 94 134
Watson, G. N. 36 46
Wave equation 27ff
waveguide (see Duct two-dimensional Duct cylindrical Half-planes two
Wedges of elastic material 173
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