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| Prilepko A.I., Orlovsky D.G., Vasin I.A. — Methods for Solving Inverse Problems in Mathematical Physics |
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| Предметный указатель |
Abstract counterpart 311
Admissible input data 490
Basis, algebraic 300
Basis, Hamel 300
Basis, orthonormal 303 508
Basis, Shauder 302
Basis, topological 302
Birkhoff-Tarsky fixed point, principle 25
Body, contact 171
Body, noncontact 172
Bolzman equation, linearized 615
Bolzman equation, nonhomogeneous 615
Bound, greatest lower 514
Bound, least upper 514
Canonical form 72
Cauchy data 106
Cauchy problem 342 350 355 442 447 478
Cauchy problem, abstract 329 586 592
Cauchy problem, homogeneous 355
Cauchy problem, nonlinear 336
Cauchy problem, uniformly well-posed 330 339 343 356 359
Cauchy sequence 301
Characteristic 76
Characteristic determinant 369
Closed two-sided ideal 307
Collision frequency 615
Completion 303
Cone 514
Contraction 310
Contraction mapping principle 271 311
Current density 637
Cyclic subspace 504
Deformation vector 592
density 126
Density of the external force 592
Density of the extraneous current 637
Density of the neutron distribution 608
Derivative, generalized 3
Derivative, partial 337
Differential scattering cross-section 614
Dirichlet boundary condition 591
Dirichlet problem 7 367
Displacement vector 591
Distance 162 301
distribution 330 615
Domain, absolutely projectively-outword-ambient 161
Domain, absolutely star-ambient 161
Eigenfunction 74
Elastic body 591
Elasticity coefficient 592
Electric charge distribution 638
Electric conductance 637
Electric field strength 637
Elliptic differential equation 365
Emission of neutrons 608
Equation, autonomous 346
Equation, Bolzman 614
Equation, first kind 308
Equation, homogeneous 330
Equation, hyperbolic 106 584
Equation, incompressibility 205
Equation, integro-functional 94
Equation, Laplace 125
Equation, Maxwell 636
Equation, nonhomogeneous 334
Equation, parabolic 10
Equation, Parseval 39
Equation, quasilinear 601
Equation, resolvent 617
Equation, second kind 309
Equation, semilinear 449
Equation, transport 607
Euler gamma-function 125
Evolution family 357
Explicit expression for the semigroup 351
Exponential growth 73
Externally contact sets 174
Fission 608
Flow, three-dimensional 206
Flow, two-dimensional 207
Formula, Cauchy — Hadamard 328
Formula, Newton — Leibniz 49 318
Formula, Ostrogradsky 582
Fourier coefficient 38 303
Fourier expansion 308
Fractional power 599
Frechet differentiable 337 353— 354
Frechet differentiable, Green 370
Frechet differentiable, Lipschitz 319
Frechet differentiable, regular 330
Fredholm alternative 43
Fredholm solvability 45
Fredholm-type property 220
Function, abstract 376
Function, analytic 328
Function, cosine 343 524
Function, sine 344 524
Function, stable 360
Functional, linear 306
Functional, positive 514
Generator of the cosine function 345
Green formula, first 124
Green formula, second 124
Green formula, third 125
Group property 366
Holder condition 319
Holder constant 4
Hypermatrix 99
Image of linear operator 304
Induction, electric 637
Induction, magnetic 637
Inequality, Cauchy 2
Inequality, Cauchy — Schwartz 2 302
Inequality, Hamack 24
Inequality, Holder 2 606
Inequality, Poincare — Friedrichs 6
Inequality, Young 2
Inner product 302
Integral of collisions 614
Integral of collisions, linearized 615
Invariant of collisions 616
Jordan’s decomposition 514
Kernel 304 322
Kronecker’s delta 88
Laplace transform 67
Lattice, Banach 514
Lattice, conditionally complete 25
Lattice, Hilbert 598
Law, Hook’s 591
Law, Ohm’s 637
Law, sreciprocity 617
linear combination 300
| Linear medium 637
Linear span 300
Magnetic field strength 637
Maxwell distribution 614
Measure, Dirac’s 503
Measure, spectral 504
Method, Cramer’s 369
Method, Fourier 38 66 308
Multiindex 3
Navier-Stokes equation, linearized 205
Navier-Stokes equation, nonlinear 206 230 254
Neumann problem 367
Neumann’s boundary condition 590
Norm 301
Norm, graph 317 493
Norm, linear operator 304
Norm, matrix 75
Operator function, differentiable 320
Operator function, strongly continuous 319
Operator, adjoint 306
Operator, anti — Hermitian 509
Operator, bounded 304
Operator, compact 307
Operator, completely continuous 307
Operator, continuous 304
Operator, contracting 63
Operator, elliptic differential 7
Operator, evolution 356 442 459 478
Operator, identity 305
Operator, integration 80
Operator, inverse 305
Operator, invertible 305
Operator, isotonic 25 57
Operator, Laplace 37 376
Operator, linear 304
Operator, nonlinear 310
Operator, positive 515
Operator, reflection 616
Operator, self-adjoint 307
Operator, Stokes 217
Operator, Sturm — Liouville 38
Operator, substitution 336
Operator, uniformly elliptic 7
Order segment 25
Orthogonal complement 303
Orthogonal decomposition 303
Orthogonal projector 303
Overdetermination, final 34 54 210 230 379 490 596
Overdetermination, integral 60 221 226 255 268 282 583 587 594 608 641
Overdetermination, pointwise 69 581
Overdetermination, singular 416 449
Perfect conductor 637
Permeability, dielectric 637
Permeability, magnetic 637
Potential, magnetic 171
Potential, power 623
Potential, simple layer 126
Potential, volume mass 126
Principle of uniform boundedness 305
Problem in variations 391
Radius of convergence 328
Regime of oscillations 592
Relation, asymptotic 445
Relation, energy 215
Relation, Gauss — Ostrogradsky 124
Relation, partial ordering 514
Rellich 7
Resolvent 305 332 335 363
Resolvent set 305
Riesz 306
Semigroup generator 332
Semigroup, analytic 340
Semigroup, compact 499 597
Semigroup, contraction 495
Semigroup, exponentially decreasing 495
Semigroup, positive 515 598
Semigroup, strongly continuous 331
Series, Fourier 39 303
Series, Neumann 79 310
Smoothing effect 379 382 440 459 477 587
Sobolev 3 4
Sobolev, vector 299
Sobolev’s embedding theory 6
Solution, classical 339 366
Solution, continuous 382 395
Solution, explicit 66
Solution, fundamental 125
Solution, generalized 20 28 34 60
Solution, strong 330 339 341—342 357 359 382
Solution, weak 11 330 339 342 357 361
Space, Banach 3 4 301
Space, dual 306
Space, Euclidean 302
Space, Hilbert 3 303
Space, Holder 4
Space, normal vector 304
Space, normed 300
Spectral decomposition 316
Spectral radius 306 370
Spectral resolution 502
Spectral type 504
Spectrum 305 314
Spectrum, continuous 306
Spectrum, discrete 508
Spectrum, point 306
Spectrum, residual 306
Spectrum, simple 504
Square root 365
Stress tensor 592
subspace 300
Successive approximation 310 435
Supersolution 22
Symmetric difference 162
System, first order 72
System, t-hyperbolic 88
System, x-hyperbolic 72
Theorem, Banach on inverse 314
Theorem, Banach — Steinhaus 304
Theorem, Birkhoff — Tarsky 25
Theorem, closed graph 314
Theorem, Hilbert — Schmidt 308
Theorem, Hille-Phillips-Y osida-Miyadera 331
Theorem, open mapping 314
Thermodynamic equilibrium 617
Two-point inverse problem 489 501
Type, hyperbolic 358 477
Type, parabolic 361 439
Volterra equation, first kind 69 321
Volterra equation, nonlinear 325
Volterra equation, second kind 69 321 353 386
Weak principle of maximum 9
wronskian 117
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