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| Evans L.C. — Partial Differential Equations |
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| Предметный указатель |
System, analytic PDE 228
System, conservation laws 567—606
System, constant coefficient, hyperbolic 408—412
System, Euler — Lagrange 437—441 453—457
System, Euler's equations 196
System, irrotational flow 197
System, ODE 176
System, reaction-diffusion 499
System, semilinear hyperbolic 573
Taylor's formula 13 31 32 226
Telegraph equation 4 190 426
Terminal-value problem, Hamilton — Jacobi equation 557
Terminal-value problem, heat equation 63
Terminal-value problem, transport equation 152
Test function 242
Traces 257—261 291
Transport equation 3 9 18—19 67
traveling wave 172 174 176 234
Traveling wave, conservation law 573 600—602
Uniqueness in calculus of variations 449
Uniqueness, backwards in time 63
Uniqueness, Cauchy problem for heat equation 58
Uniqueness, conservation law 151 607
Uniqueness, Hamilton — Jacobi equation 132—135
Uniqueness, heat equation 62
Uniqueness, Poisson's equation 27
Uniqueness, quasilinear elliptic equation 497
Uniqueness, viscosity solution 547
Value function 552
Vanishing viscosity method 204 205 540 543 605
Variational formulation 296
Variational inequality 467—470 489 537
Version of a function 269
Viscosity solution 539—565
Viscosity solution, definition of 542
Viscosity solution, existence 550
Viscosity solution, uniqueness 546 547
Wave equation 4 9 65—85 173
| Wave equation, d' Alembert's formula 68
Wave equation, derivation 66
Wave equation, dimension, even 78—80
Wave equation, dimension, odd 74—78
Wave equation, dimension, one 19 67—69 75
Wave equation, dimension, three 71—73
Wave equation, dimension, two 73—74
Wave equation, equipartition of energy 88
Wave equation, generalized 4
Wave equation, Kirchhoff's formula 73
Wave equation, method of descent 74 79
Wave equation, nonhomogeneous 65
Wave equation, nonlinear 5 569 578
Wave equation, Poisson's formula 74
Wave speeds 172 401
Wave, N- 159
Wave, plane 172 401
Wave, rarefaction 141 582
Wave, shock 143 573 583 589 599 600 604
Wave, simple 579
Wave, traveling 172 174 176 234 573 600—602
Weak continuity of determinants 454
Weak convergence 444 495 540 639
Weak partial derivative 242—254
Weak partial derivative, definition of 242
Weak partial derivative, examples of 243—244 246—247
Weak partial derivative, properties of 247—248
Weak partial derivative, uniqueness of 243
Weak solution, conservation law 150—154 570 607
Weak solution, Euler — Lagrange equation 450
Weak solution, first-order hyperbolic system 401 403
Weak solution, Hamilton — Jacobi equation 129—136
Weak solution, second-order elliptic equation 295—307
Weak solution, second-order hyperbolic equation 378—387
Weak solution, second-order parabolic equation 351—358
Weak solution, transport equation 19
Weakly measurable function 649
Well-posed problem 7 234
Yosida approximation 526 530
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