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Stakgold I. Ч Boundary value problems of mathematical physics
Stakgold I. Ч Boundary value problems of mathematical physics



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Ќазвание: Boundary value problems of mathematical physics

јвтор: Stakgold I.

јннотаци€:

For more than 30 years, this two-volume set has helped prepare graduate students to use PDEs and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Contains many concrete examples of boundary value problems for PDEs that still cover a variety of modern applications


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1987

 оличество страниц: 748

ƒобавлена в каталог: 23.10.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Addition theorem for cylindrical waves      268
Addition theorem for Legendre functions      398
Addition theorem for spherical waves      290
Adjoint      9 198
Admissible functions      332
Approximation in subspace      335Ч336
Aronszajn, N.      382
Asymptotic expansions for heat equation      206 222 236
Asymptotic expansions of eigenvalues of Laplacian      231Ч234 239Ч240
Asymptotic expansions of integrals      399Ч402
Base operators      382
Bazley, N.W.      382
Bessel equation      242 268Ч270 295
Biharmonic equation      40 105 365
Boundary conditions, essential      353
Boundary conditions, natural      352Ч355
Boundary value problem      88
Boundary value problem, well-posed      89
Capacity      171Ч174 350Ч352
Cauchy data      74
Cauchy problem      73
Causal function      see "Right-sided function"
Causal fundamental solution      see "Fundamental solution"
Characteristic      74
Characteristic of wave equation      46
Characteristic, surface      74
Classification of partial differential equations      73Ч87
Comparison theorem      377
Composite medium      183 234Ч293
Conductor      171Ч183
Consistency condition      171
continuous dependence on data      89 91 95 102Ч103 226
Convolution      18Ч20 49
Cylindrical wave      267Ч268
d'Alembert's formula      85
Damped wave equation      65Ч69 257Ч259 264
Delta function      5 20 27 34
Descent, method of      255
Diaz, J.      344
Difference kernel      311
Diffraction      see "Scattering"
Diffusion      230 240Ч241 329 see
Dipole      6 111 201
Dipole layer      12 113
Dirichlet problem      90Ч103 122Ч125 135 142 172 296 348
Dissipative wave equation      see "Damped wave equation"
Distributions of slow growth      31 37
Distributions, action of      4
Distributions, convergence of      10Ч16
Distributions, convolution of      18
Distributions, definition of      4 31 37
Distributions, differentiation of      7
Distributions, dipole      6 8
Distributions, Dirac      5
Distributions, direct product of      17
Distributions, partial differential equations for      39
Distributions, product of functions and      7
Distributions, regular      5
Distributions, singular      5
Distributions, translation of      5
Distributions, values of      9
Divergence theorem      89
Eigenfunction expansion for heat-conduction equation      213Ч218
Eigenfunction expansion for Laplace's equation      153Ч164
Eigenfunction expansion for wave equation      248 252
Eigenvalues of negative Laplacian      136Ч142
Eigenvalues, asymptotic distribution of      231 239Ч240
Eigenvalues, comparison theorem for      377
Eigenvalues, extremal principles for      369Ч392
Eigenvalues, lower bounds to      381Ч392
Elliptic equations      80
Energy flux      262 303
Energy inner product      342
Energy integral for heat conduction      225
Energy integral for wave equation      244 261Ч262
Energy norm      343
Entire functions      315
Extremal principles for capacity      350Ч352
Extremal principles for eigenvalues in Hilbert space      372Ч392
Extremal principles for eigenvalues in n space      369Ч372
Extremal principles for functional      337Ч340 352Ч355 358Ч361
Extremal principles for torsional rigidity      346Ч348
Extremal principles, complementary      344Ч352
Fluid flow      185Ч190
Fokker Ч Planck equation      230
Fourier integral theorem      23
Fourier transforms and Wiener Ч Hopf equations      311Ч331
Fourier transforms of distributions      30Ч39
Fourier transforms of functions      23
Fourier transforms of test function      31
Fox, D.W.      382
Free boundary      237
Friedrichs, K.O.      344
Functionals      3 332
Functionals, continuity of      3
Fundamental solution      48
Fundamental solution of damped wave equation      65Ч69
Fundamental solution of heat-conduction equation      58Ч60 198
Fundamental solution of Helmholtz's equation      53Ч58 266Ч267
Fundamental solution of Laplace's equation      49Ч53
Fundamental solution of wave equation      61Ч65 249 253Ч256
Fundamental solution on Riemann surface      270Ч272
Fundamental solution, pole of      48
Generalized functions      see "Distributions"
Generalized solution      42
Green's function      see also "Fundamental solution"
Green's function for heat conduction      198 204 209Ч218
Green's function for Helmholtz's equation      265Ч290
Green's function for Laplace's equation      130Ч171
Green's function for wave equation      246Ч252
Green's theorem      40 89
Hadamard, J.      255
Hankel functions      see "Bessel equation"
Hankel transform      275Ч280
Harmonic functions, maximum principle for      101
Harmonic functions, mean value theorem for      99
Heat-conduction equation      81 194Ч243 280Ч281
Heat-conduction equation in composite medium      234Ч237
Heat-conduction equation, backward      229
Heat-conduction equation, causal fundamental solution      58Ч60
Heat-conduction equation, causal Green's function for      197Ч222
Heat-conduction equation, energy integral for      223
Heat-conduction equation, Green's theorem for      41 196
Heat-conduction equation, ill-posed problems for      229
Heat-conduction equation, maximum principle for      224Ч225
Heat-conduction equation, Stefan problem for      237Ч238
Heat-conduction equation, uniqueness for      225Ч226
Helmholtz's equation in exterior domain      294Ч311
Helmholtz's equation in wedge      272Ч273
Helmholtz's equation, fundamental solution of      53Ч58
Helmholtz's equation, Green's function for      265Ч285
Helmholtz's equation, half-plane problem for      281Ч290 321Ч327
Helmholtz's equation, mean value property      105
Hilbert Ч Schmidt kernels      135 375
Huyghens' principle      256
Hyperbolic equations      80Ч85
Images      149 166Ч169 204 209 211 251 252
Incident field      299
Initial data      72
Initial value problem      73
Integral equations for capacity      172Ч174 351
Integral equations for scattering problems      301
Integral equations of potential theory      122Ч130 146 171Ч193
Integral equations of Wiener Ч Hopf type      311Ч331
Integral equations with difference kernel      311Ч331
Integrodifferential equation      366Ч367 389Ч390
Interior operator      74
Intermediate problems      382
Jones, D.S.      368
Kantorovich Ч Lebedev transform      273
Kirchhoff's formula      263
Klein Ч Gordon equation      70
Laplace transform      38 206 218 236 249 401Ч402
Laplace's equation      40 49Ч53 88Ч192 see
Laplace's equation in two dimensions      128
Laplace's equation, eigenvalue problem for      136Ч142 231Ч234
Laplace's equation, exterior Dirichlet problem for      123 129 142
Laplace's equation, fundamental solution of      49Ч53
Laplace's equation, Green's function for      130Ч171
Laplace's equation, Green's theorem for      40
Laplace's equation, interior Dirichlet problem for      122 128 135
Laplace's equation, Neumann problem for      126 128
Layers, double      12 113
Layers, simple      7 39 112
Layers, surface      7 12 110Ч121
Least squares      361Ч363
Left-side function      28
Legendre functions      393Ч398
Levine, H.      283 311 340 357
Limiting absorption      259Ч261
Locally integrable      2
Macdonald function      266 279 321
Mapping function      164
Maximin theorem      371
Maximum Principle for harmonic functions      101
Maximum principle for heat conduction      224
Maximum theorem for functionals      337
Mean value property for biharmonic equation      105
Mean value property for Helmholtz equation      105
Mean value property of harmonic functions      99
Mehler's integral representation      284
Mellin transform      167 169
Minimax theorem      371
Monochromatic excitation      259Ч261
Multiindex      2
Neumann problem      126 128 171 185Ч191
Neumann problem and fluid flow      185Ч191
Neumann problem, consistency condition for      171
Neumann problem, extremal principles for      363Ч364
Null sequences      3 30 36
One-sided functions      28
Operators, base      382
Operators, bounded above      372
Operators, bounded below      372
Operators, completely continuous      133Ч135 375
Operators, Hilbert Ч Schmidt      135 375
Operators, indefinite      355Ч357
Operators, integrodifferential      366 389Ч390
Operators, interior      74
Operators, nonnegative      336
Operators, nonsymmetric      355Ч357
Operators, positive      337 358
Operators, self-adjoint      9 376
Operators, semibounded      372
Operators, strongly positive      343 363
Operators, symmetric      337
Parabolic equations      80
Parseval formula      24
Partial differential equations      88Ч311
Partial differential equations for distributions      39Ч48
Partial differential equations of first order      76Ч79
Partial differential equations of second order      79Ч87
Partial differential equations, classification of      73Ч87
Partial differential equations, elliptic      80
Partial differential equations, fundamental solutions of      48Ч72
Partial differential equations, hyperbolic      80
Partial differential equations, parabolic      80
Plane wave      285Ч286 302
Poisson equation      103 345
Poisson kernel      95
Poisson sum formula      212
Pole of fundamental solution      48
Potential theory      88Ч193 267 see
Projection operator      335Ч336
Propagation of discontinuities      46 77
Radiation condition      297
Rayleigh quotient      369
Rayleigh Ч Ritz procedure      see "Ritz Ч Rayleigh"
Reciprocity principle      303 342 368
Rellich, F.      297
Retarded potential      254
Riemann mapping theorem      164
Riemann surface      270
Right-side function      28
Ritz Ч Rayleigh, equations      341 363 366Ч368
Ritz Ч Rayleigh, procedure      332 334 340Ч343 362 377Ч378
Scattered amplitude      304
Scattered field      300
Scattering      299Ч311 328
Scattering cross section      303
Scattering cross section, stationary principle for      309
Schwarz constants      380
Schwarz inequality      344
Schwinger Ч Levine principle      311 340 357
Self-adjoint      9 376
Semigroups of operators      227
Slow growth, distribution of      31 37
Slow growth, functions of      29
Sokolnikoff, I.S.      346
Sommerfeld, A.      277 297
Spherical harmonics      109 126 127 144 290 295 393Ч398
Spherical wave      267 290
Stationary principles for indefinite operators      356
Stationary principles for nonsymmetric operators      357 367Ч368
Stationary principles for scattering cross section      309Ч311
Steady heat conduction      88 183
Stefan Problem      237
Strict solution      42
Support      2
Symbolic functions      see "Distributions"
Tangential derivative      74
Telegraphy equation      65 258
Test functions      3
Test functions of rapid decay      30 36
Test functions, convergence of      3 30
Test functions, null sequences of      3 30 36
Theta function      212
Torsional rigidity      346Ч348
Transversal      41
Uniqueness theorem for heat conduction      225Ч226
Uniqueness theorem for Helmholtz's equation      296Ч299
Uniqueness theorem for Laplace's equation      102
Uniqueness theorem for wave equation      243
variation-iteration      380Ч381
Variational methods      see "Extremal principles" "Stationary
Wave equation      81 194 196Ч197 243Ч265 289Ч294
Wave equation in composite medium      293
Wave equation, d'Alembert's solution of      85
Wave equation, damped      65Ч69 257Ч259 264
Wave equation, fundamental solution of      61Ч65
Wave equation, generalized solution of      44
Wave equation, Green's function of      246Ч256
Wave equation, Green's theorem for      41 47 197
Wave equation, method of descent for      255Ч256
Wave guide      291
Weber transform      242
Weinstein, A.      382
Well-posed problem      89
Wiener Ч Hopf equation      311Ч331
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