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Lions J-L., Dautray R. — Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational Methods
Lions J-L., Dautray R. — Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational Methods

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Название: Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational Methods

Авторы: Lions J-L., Dautray R.

Аннотация:

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 608

Добавлена в каталог: 12.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
3-point scheme      84
Abstract variational problem      375
Accretive boundary value problem      453
Accretive extension      372
Accretive operator      372
Adjoint operator      353 361
Adjoint sesquilinear form      353
Algebra      497
Algebra of convolutions      497
Algebra of distributions      498
Algebra, Banach      318n
Algebra, normed      318n
Analytic semi-groups      225
Analyticity of solutions      234
Antidual of a topological space      281
Antilinear form      281
Automorphisms of $\mathbb{R}^{n}$      518
Babuska's paradox      424
Backward Cauchy problem      204 223
Baire's lemma      276
Baire's property      276
Ball      271
Banach algebra      318n
Banach space      272
Banach — Steinhaus theorem      275
Banach's approximation problem      330
Bessel functions      42
Bessel functions, integral representation      43
Bessel functions, recurrence relations      43
Bessel — Parseval Inequality      302
Bessel's equation      42
Bicharacteristic      159
Bicharacteristic curve      161
Bicharacteristic solution      160
Bidual      285
Biharmonic equation      55
Biharmonic operator      450
Bijection      539n
Bilinear form      292
Bochner — Schwartz theorem      526
Bounded operator      274
Cauchy problems      164 204 209 214 217
Cauchy sequence      272
Cauchy — Kowalewsky theorem      164
Cauchy — Riemann operator      176 188
Cauchy — Schwartz inequality      121 293
Cayley transform      362
Cesaro mean      17
Cesaro summability      15
Characteristic cone      158
Characteristic hyperplane      157
Characteristic polynomial      171
Characteristic vector      157
Characteristics      157
Characteristics, multiple      159
Characteristics, simple      159
Chinese remainder theorem      71
Closable operator      335
Closed graph theorem      280
Closed image theorem      348
Closed operator      335 361
Closure of an operator      335
Codimension      307
Coercive sesquilinear form      368
Collocation method      80
Compact operator      123
Compactness (weak)      289
comparison of operators      241
Comparison principle      261
Complete family      300
Complete metric space      272
Composition of operators      307 316
Cone, future      492
Cone, past      492
Constant force operator      245
Continuity      332
Continuous operator      274
Contraction      297n
Convergence of operators      313
Convergence, strong      287 317
Convergence, weak      287 318
Convergence, Weak-star      290
Convex set      285
Convexity inequalities      133
Convolution algebra      497
Convolution of distributions      492
Convolution of functions      458
Convolutive support      496
Convolutor      521
Cooley — Tukey transform      64
Cracks      406
Cyclic convolution      69
Cyclic convolution of order 2      72
Cyclic convolution of order 3      73
Cyclic convolution of order 6      75
d'Alembertian      180 230
Decomposable operator      190
Degenerate operator      322
density      273 461
Denumerable total family      300
Diagonalisation of operators      15 25 29 51
Differentiability      332
Differential quotients, method of      430
Differentiation in $L^{p}$      338
Diffusion of neutrons      440
Dirac distribution      466
Dirac distribution on a surface      487
Dirac measure      466
Dirac measure, primitives of      482
Dirac's periodic distribution      9
Direct Cauchy problem      205 223
Dirichlet problems      17 20 32 53 112 379
Dirichlet's lemma      6n
Discrete Fourier Transform      59
Discretisation of Poisson problem      84
Displacement operators      319
Dissipativity      251
Distance      272
Distributions of positive type      525
Distributions of rapid decay      521
Distributions of slow growth      507
Distributions with compact support      475
Distributions with convolutive support      496
Distributions, bounded      526n
Distributions, convolution of      492 494
Distributions, differentiation of      467 488
Distributions, homogeneous      519
Distributions, invariant under rotation      489
Distributions, invariant under translation      489
Distributions, normal space of      97
Distributions, periodic      7
Distributions, positive      467
Distributions, restriction of      474
Distributions, tempered      507
Distributions, tensor product of      480
Division problem      483
Domain of a linear operator      305
Domain of dependence      210
Dual of a topological space      281
Elasticity operator      419
Elastostatics      411
Elementary solution of an operator      149 183
Elliptic problems of 2nd order      393
Energy space      269
Equivalent norms      280
Equivalent semi-norms      271
Estimates of analyticity      237
Euler's relation (identity)      160 519
Extension by reflexion      117
Extension of a linear operator      282 307
Extension, canonical      116
Extension, m-extension      114
Family, complete      300
Family, orthonormal      299
Family, total      300
Fast Fourier transform in two dimensions      77
Fast Fourier transform of Cooley and Tukey      64
Fast Fourier transform of Good and Winograd      66
Fast Fourier transform, applications      78
Fast solvers for Laplacian      84
Finite part      469
Five-point scheme      85
Flexure of plates      420
Force of an operator      242
Form, antilinear (or semi-linear)      281
Form, bilinear      292
Form, linear      281
Form, sesquilinear      292 351 367
Forward Cauchy problem      204
Fourier coefficient      5 10 301
Fourier cotransform      501
Fourier inversion formula      503
Fourier transforms      356 500
Fourier transforms in $L^{1}$      500
Fourier transforms in $L^{2}$      506
Fourier transforms in $\mathbb{R}^{n}$      56
Fourier transforms of distributions with compact support      509
Fourier transforms of measures      523
Fourier transforms of tempered distributions      506
Fourier transforms, calculation of      510
Fourier transforms, fast      61 64 66
Fourier transforms, partial      513
Frechet space      272
Fredholm alternative      378
Fredholm operator      348
Function of positive type      525
Function of rapid decay      502
Function of slow growth      523
Fundamental solution      183n
Future cone      492
Galerkin method      374
Garding's inequality      389
Gevrey class      240
Global regularity      426 437
Good — Winograd transform      66
Graph of an operator      306
Green — Ostrogradski formula      379
Green's function      441 445
Green's kernel      441
Hahn — Banach theorem      282 374
Hamiltonian system      160 192
Hankel transform      2 40 47
Hankel transform, table of      57
Hankel — Bochner transformation      56n
Harnack estimate      267
Harnack's inequality      250
Heat operator      192
Hermitian form      357
Hermitian operator      353
Hermitian scalar product      291
Hermitian symmetry      353
Hilbert space      291
Hilbert space, separable      300
Hilbert — Schmidt operator      357
Holmgren's theorem      166
Holomorphic semi-groups      225
Holomorphy      305
Homeomorphism      321n
Hyperbolic operator      190
Hyperbolic operator of order 2      198
Hypoellipticity      177 230
Image of a distribution      481
Image of a linear operator      305
Inclusion properties      461
Indices of deficiency      307
Indices of nullity      307
Inductive limit in Frechet spaces      273
Inequalities in Sobolev spaces      125
Inequality of Cauchy — Schwarz      293
Inequality of Garding      389
Inequality of Korn      414
Inequality of Poincare      126
Inequality of Young      459
Infinite matrices      311 323 338 352
Injection      539n
Injection of Sobolev      139
Injective mapping      539n
Integral operators      312 319 324 352 360
Integro-differential forms      398
Interpolate      60
Invariance under translation      272
Inverse image      481 485
Invertibility of operators      319
Involutive mapping      323
Isometric operator      355
Isometry      41 355
Kernel of a linear operator      305
Korn's inequality      414
Landau's notation      523n
Laplace operator      173
Laplace — Beltrami operator      147 156
Laplacian      173
Lax — Milgram Theorem      368 376
Leibniz's formula      152 476
Lifting operator      110
Linear differential equations      479
Linear differential operators      148
Linear form      281
Local operator      149
Local regularity of solutions      230
Locally finite operator      149
Lorentz group      491
Love — Kirchhoff theory      420
M-extension      114
Matrices, infinite      311 323 338 352
Maximum principles      251 259 265
Measure of mass +1      466
Measure of slow growth      523
Measure, absolutely continuous      466
Measure, density of      466
Measure, positive      467
Measure, summable      465
Measure, tempered      523
Meixner's condition      37
Mellin transform      2 24
Mellin transform, table of      40
Mixed problem      394
Monomial pseudo-functions      471
Multiplicator      520
Mutually transposed operators      309
Neumann problems      380 448
Neumann series      320
Neutrons, global balance of      410
Newtonian potentials      185n
Nikodym open sets      129
Non-local boundary conditions      397
Norm      270
Normal space of distributions      97
Normed algebra      318n
Normed vector space      272
Nuclear operator      331
Nullity      307
One-parameter semi-groups      226
Open mapping theorem      278
Operator in Banach or Hilbert spaces, adjoint      353 361
Operator in Banach or Hilbert spaces, bounded      274 325
Operator in Banach or Hilbert spaces, compact      327
Operator in Banach or Hilbert spaces, continuous      274
Operator in Banach or Hilbert spaces, degenerate      322
Operator in Banach or Hilbert spaces, Fredholm      348
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