Neittaanmaki P., Tiba D. — Optimal Control of Nonlinear Parabolic Systems: Theory, Algorithms and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Neittaanmaki P., Tiba D. — Optimal Control of Nonlinear Parabolic Systems: Theory, Algorithms and Applications

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Название: Optimal Control of Nonlinear Parabolic Systems: Theory, Algorithms and Applications

Авторы: Neittaanmaki P., Tiba D.

Аннотация:

Presenting the numerical methods necessary to computerize optimal control processes, this reference discusses theoretical approaches to the study of optimal control problems governed by nonlinear parabolic systems, including semilinear equations, variational inequalities, and systems with phase transitions. Several examples are worked out in detail to demonstrate the usefulness of the proposed methods. To make the book more accessible, brief presentations of linear or nonlinear evolution equations, numerical approximation via finite elements, and convex control problems are included.

Язык:

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 399

Добавлена в каталог: 23.04.2005

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Предметный указатель

$C_0^{\infty}(\Omega)$ , $C^{m}(\bar{\Omega};X)$       xiii 32
$H^k(\Omega)$ , $H^{k,2}(\Omega)$ , $H^{k,2}(Q)$       xiii 32
$H^s(\Gamma)$       33
$L^p(\Omega)$ , $L^p(\Omega,X)$       xiii 31
      xiii
$Q = \Omega\times]0, T[$       xiii
$W_0^{k,p}(\Omega)$ , $W^{-k,p}(\Omega)$ , $W^{k,p}(\Omega)$ , $W^{2,1,p}(\Omega)$       xiii 32
$\mathcal{D}(\Omega)$ , $\mathcal{D}'(\Omega)$       xiii 32
Adams, R.      35 377
Adapted penalization      172
Adjoint system      171 186 228 239
Admissibility      186 336
Admissibility condition      356
Admissible control      25 185
Admissible control, $\delta$ -      337
Admissible set      3 185
Ahmed N.U.      183 377
Algebraic equation      89
Algorithm, augmented Lagrangian      364
Algorithm, bundle      306
Algorithm, descent      232
Algorithm, gradient      234 265 290
Alifanov, O.      6 377
Alt, W.      226 377
Ames, W.F.      61 188 377
Arnautu, V.      73 226 261 263 296 299 303 377
Arrhenius law      29
Artyukhin, A.      6 377
Atthey, D.R.      77 377
Aubin — Nitsche trick      97
Aubin, J.P.      35 42 198 290 377
Aziz, A.K.      97 377
Babuska, I.      97 377
Baiocchi transformation      61
Baiocchi, C.      v 56 377
Banach space      31
Bang-bang, control      180 298 302 349
Banichuk, N.V.      168 377
Banks, H.T.      6 183 377
Barbu, V.      v 36 44 46 52 64 65 66 68 72 73 75 76 128 164 172 179 182 197 209 210 215 217 220 226 251 253 258 261 296 299 303 319 322 324 377 378
Barron, A.N.      217
Basis function      84
Beberness, J.W.      184 378
Benilan, Ph.      63 378
Berger, A.E.      12 378
Bergounioux, M.      355 378
Bermudez, A.      28 63 79 226 316 378 379 386 387
Bicos, A.S.      4 379
Bicubi, basis function      84
Bilinear form, coercive      48
Bilinear form, symmetric      48
Billet      17
Birat, J.P.      22 384
Blum, J.      223 225 379
Bolza problem      165
Bonnans, J.F.      164 185 197 226 326 355 379 388
Bossavit, A.      17 379
Boundary condition, Dirichlet      5
Boundary condition, mixed      49
Boundary condition, Neumann      47
Boundary condition, Newton      47
Boundary value problem, multiphase      8
Boundary value problem, nonlinear      28
Boundary value problem, one-phase Stefan      9
Boundary value problem, two-phase      8
Boundary, Lipschitz      33
Boundary, smooth      34
Brezis, H.      19 35 36 44 63 68 127 179 188 343 379
Bundle method      274
BV(0, T;X)      xiii
Caffarelli, C.A.      61 79 379
Caginalp, G.      79 379
Cannon, J.R.      13 379
Capelo, A.      v 377
Casas, E.      326 355 379
Casting process      20
Cea, J.      237 380
Cea’s lemma      95
Centroit rule      87
Chain rule      39
Characteristic function      57
Chen, Z.      148 214 380 382
Ciarlet, Ph.      85 88 99 103 133 137 380
Ciavaldini, J.F.      84 380
Ciment, M.      12 378
Clarke, F.H.      45 210 274 322 325 380
Classical solution      47 54
Coercive operator      39
Compatibility condition      54
Concentration      2 17
Cone      43
Conjugate gradient method      247
Conrad, F.      17 380
Continuous casting      19
Contraction mapping      39
Control constraint      2 30 165
Control problem      2 24 27 30 164 218
Control problem, state constrained      319
Controllability      217
Convergent      232
Correa, R.      45 380
Cournil, M.      17 45 380
Crandall, M.G.      63 380
Crank — Nicolson scheme      101
Crank, J.      125 380
Crowley, A.B.      17 79 380
Crystal growth model      16
Crystal growth model, dissolution model      16
Dautray, R.      34 50 380
Decomposition of domain      81
Demicontinuous      39
Derivative, directional      38
Derivative, distributional      32
Descent algorithm      232
DiBenedetto, E.      61 73 78 79 339 340 343 380
Differentiable, Frechet      39
Differentiable, Gateaux      38
Differentiable, weakly      38
Diffusion      1
Directional derivative      38
Directional differential      38
Discretization      83
distribution      33
DOM      xiii
Domain, Lipschitz      34
Domain, polygonal      81
Domain, rectangular      85
Dual space      32
Duality mapping      42
Duvaut, G.      56 61 381
Ekeland, I.      326 381
Elastoplastic torsion      18
Element      81 82
Element, Lagrange      83
Element, prismatic      82
Element, rectangular      82
Element, triangular      81
Elimination formulae      92
Elliott, C.M.      v 11 63 79 142 148 246 279 381 386
Ellipticity assumption      47
Emission factor      21
Energy functional      49
Energy norm      49
Enthalphy      14 21 178
Equation, Fourier      26
Equation, heat conduction      20
Equation, Laplace      47
Equation, parabolic diffusion      18
Equation, Poisson      47
EQUIVALENCE      335

Eriksson, K.      116 381
Error, consistence      111
Error, estimate      96
ess supp      32
Evans, L.C.      79 379
Evolution variational inequality      68
Exterior normal      xiv 6
Fasano, A.      12 381
Federer, H.      78 381
FEM      80
Fetter, A.      131
Fife, D.C.      79 386
Filippov, U.M.      63 381
Fix, G.      97 387
Fleming, W.H.      165 381
Fletcher, R.      241 381
Fortin, M.      364 381
Fourier equation      26
Fourier transform      33
Frechet differentiable      39
Free boundary      7 10 13
Free boundary, problem      7 18 278
Fremond, M.      56 61 381
Friedman, A.      v 6 32 54 61 77 78 217 381 382
Friedrich’s inequality      49
Friedrich’s mollifier      196
Function, characteristic      57
Function, closed      36
Function, indicator      62
Function, Lipschitz      33
Function, proper      36
Function, test      47
Function, trial      47
Functional      32
Functional, energy      49
Functional, quadratic      48
Galerkin, approximation      253 270
Galerkin, method      88
Gateaux differentiable      38
Generalized gradient      45
George, P.L.      82 382
Gilbarg, D.      50 382
Gill, Ph.E.      241 382 383
Glashoff, K.      302 382
Global regularity      50
Glowinski, R.      19 57 133 137 364 381 382
Goering, H.      99 382
Goh, C.J.      v 239 382 387
Gotz, I.G.      79 382
Gradient algorithm      234 264 290
Gradient formula      264 265
Gradient method      233
Gradient, Clarke      45 275
Gradient, generalized      45 275
Graph, maximal monotone      56
Green formula      47
Grisvard, P.      50 382
Gronwall lemma      36
Gruver, W.A.      237 302 382
Hachbusch, W.      226 382
Haslinger, J.      v 164 333 382
He, Z.X.      217 324 382
Heat conductivity      5
Heat conductivity, conduction equation      20
Henry, J.      22 384
Hermite interpolation      85
Hewitt, E.      32 382
Hilbert space      31
Hill, C.D.      13 379
Hoffmann, K.-H.      148 214 226 296 382 383
Hokkanen, V.      76 383
Identification of free boundary      221
Identification of parameter      5
Indicator function      43 62
Induction heating      17
Inequality, Friedrichs      49
Inequality, Minkowski      110
Initial condition      21
Interpolant      84
Interpolation, Hermite      85
Interpolation, Lagrange      85
Inverse, problem      6
Inverse, Stefan problem      217 295
Inverse, temperature model      304
Jensen, S.      17 383
Jiang, L.      214 217 381 382
Jofre, A.      45 380
Johnson, C.      99 116 117 381 383
Kamenomotskaja, S.L.      60 383
Kardestuncer, H.      82 85 383
Kassay, D.R.      184 378
Kenmochi, N.      16 383
Kernevez, J.P.      1 383
Kinderlehrer, D.      v 35 78 383
Kirchhoff tranformation      3 14 22 178
Kiwiel, K.C.      274 383
Knowles, G.      226 383
Komornik, V.      187 388
Krabs, W.      226 383
Krizek, M.      88 96 98 132 383
Kronecker symbol      47
Kunish, K.      6 182 377
Kupfer, F.S.      316 383
Kuribayashi, T.      304 386
Ladyzenskaya, O.A.      50 54 185 332 383
Lagrange, element      83
Lagrange, interpolation      85
Lagrange, method      355
Lagrange, multiplier      356
Laitinen, E.      17 22 156 158 161 192 308 314 383 384 385
Lamp, U.      226 383
Laplace equation      47
Larrecq, M.      22 384
Lasiecka, I.      55 226 384
Latent heat      20
Lesaint, P.      119 124 304 384
Lewis, F.L.      v 384
Limit, strong      31
Limit, weak      31
Lions, J.L.      v 19 33 34 35 44 50 54 55 57 61 75 137 164 166 183 184 200 222 331 341 344 380 382 384
Lipschitz, boundary      33
Lipschitz, constant      33
Lipschitz, domain      34
Lipschitz, mapping      33
Liquid pool      20
Load vector      90
Louhenkilpi, S.      158 161 314 384
Mackenroth, U.      226 377 384
Magenes, E.      11 33 54 222 344 384
Makela, M.      v 275 293 307 384
Makinen, R.      220 388
Malanovski, K.      226 244 385
Mannikko, T.      164 244 355 378 385 388
Mapping, contraction      39
Mapping, duality      42
Mapping, Lipschitz      33
Martinez, A.      28 316 378
mass density      5
Matrix, mass      91 100
Matrix, stiffness      90 101
Maximal monotone graph      56
Maximal monotone operator      38
Maximum principle      171 186 210 228 264
Maximum principle, discrete form      230
Meas      xiii
Meike, Z.      388
Meirmanov, A.      63 79 385
Method, bundle      274
Method, conjugate gradient      247
Method, Crank — Nicolson      101

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