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Lifanov I.K., Poltavskii L.N., Vainikko G.M. — Hypersingular integral equations and their applications
Lifanov I.K., Poltavskii L.N., Vainikko G.M. — Hypersingular integral equations and their applications

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Название: Hypersingular integral equations and their applications

Авторы: Lifanov I.K., Poltavskii L.N., Vainikko G.M.

Аннотация:

A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical and exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and consider one-, two - and multi-dimensional integral equations. The text also presents the discrete closed vortex frame method and some other numerical methods for solving hypersingular integral equations. The treatment includes applications to problems in areas such as aerodynamics, elasticity, diffraction, and heat and mass transfer.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 396

Добавлена в каталог: 15.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Admissible neighborhood      318
Analytic generalized function      39
Angular nodes      1
Antenna-diffraction problems      372
Calculated time instant      336
Canonical grid      121
Canonical partition      121 247 249
Cauchy integral      9
Cauchy principal value of an integral      3
Chaplygin — Zhukovskii — Kutta condition      342
Characteristic function of an operator      10 57 123 216
Characteristic hypersingular equation      207
Compactly supported function      32
Contact problem      381
Convolution      27 32 34 122 123
Coordinate neighborhood      53
Delta-function      28
Density function      10
Difference ratio      301
Diffraction problems      208
Direct value of a function on a curve      323
Direct value of the double layer potential      329 360
Direct value of the normal derivative      331
Direct value of the tangential derivative      333
Dirichlet problem      205
Discrete Fourier transformation      121 122
Discrete Green function      215 217 222
Discrete one-dimensional singular operators      171
Discrete Prandtl operator      215
Discrete singular operator      169 171
Discrete vortex operator      176 198
Distributed vortex intensity      335
Double layer potential      116 329 359
Elliptic operator      81
Elliptic symbol      84
Exterior Neumann problem      115
Family of discrete singular operators      176
Finite part in the sense of Hadamard      4
Finite problem of restriction      222
Flow past an airfoil      309 334
Fourier transform      34 35
Fractional quotient      131
Framework      9
Fredholm operators      80
Generalized function      28 30 53
Generalized solution      115
Grid Fourier transform      122
Grid functions      121
Helmholtz equation      208 283 376
Hilbert integrals      4 247
Holder condition      2
Homogeneous factorization      86
Homogeneous function      56
Hypersingular Hilbert integrals      4
Hypersingular integral equation      77
Hypersingular operator      202
Index of an operator      78
Infinitely differentiable manifold      53
Integral in the sense of Hadamard      99 117
Integral projector      139
Interior point      9
Inverse Fourier transform      34
Iterated difference Laplace operator      200
Iterated Laplace operator      207
Jet discharge      334
Kinematic compatibility      342
Left regularizer      79
Lipschitz boundary      51 149
Lipschitz family of step functions      203
Lyapunov curve      2
Multhopff equation      291
Multiple singular integral      9
Neumann kernel      23
Neumann problem      95 283 376
Noetherian operator      78 119
Noetherian property      105
Non-penetration condition      309 342
Nonstationary flow      361
Normal coordinate system      11 99
Normal neighborhood      260
Normally resolvable operator      78
Normally starshaped domain      157
Odd generalized function      38
Operator of finite order      179
Operator of restriction      181
Operators of Prandtl type      218
Parseval identity      34
Partition      157
Piecewise smooth curve      1
Poisson kernel      23
Pole      57
Potential theory      317 348
Prandtl operator      105 111
Principal value      10
Problem of flow with suction      17
Problem of restriction      211 222
Pseudodifferential equation      77
Pseudodifferential operator      55 59 125
Punch problem      381
Quadrature formulas      184 188 189
Quotient spaces      271
Rectangular set of indices      232
Regular functional      28
Restriction of a functional      30
Restriction of a pseudodifferential operator      211
Restriction of an integral projector      157
Riesz operators      58
Right difference operator      177
Right regularizer      79
Shift of a generalized function      29
Ship deck      361
Simple layer density      330
Simple layer potential      330 361
Singular integral      57
Singular integrals in the sense of Hadamard      58
Singular solutions      6
Smooth closed curve      1
Smooth open-ended curve      1
Smooth simple line      1
Sobolev imbedding theorem      134
Sobolev — Slobodetskii spaces      42 53
Space of fractional quotients      131
Space of step functions      136-138 148
Special coordinate system      96 117
Special local Cartesian coordinate system      51
Spherical functions      377
Stable family of operators      193
Stable neighborhood      51
Standard map      121
Step Fourier transformation      121
Suction      309 334
Support of a functional      30
Symbol of operator      46 55
Symbol of the convolution operator      123
Topology in S      27
Weak approximation      178 179
Weak convergence      287
Weighted spaces      164
Wide-band antenna      367
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