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Vrabie I.I. — Compactness methods for nonlinear evolutions
Vrabie I.I. — Compactness methods for nonlinear evolutions



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Название: Compactness methods for nonlinear evolutions

Автор: Vrabie I.I.

Аннотация:

This monograph provides a self-contained and comprehensive account of the most significant existence results obtained over the
past two decades referring to some remarkable classes of ill-posed problems governed by non-accretive operators. All the results are derived from several compactness arguments, due mainly to the author, and are suitably illustrated by examples arising from various concrete problems - for example, nonlinear diffusion, heat conduction in materials with memory, fluid dynamics, and vibrations of a string with memory. Reference is made to optimal control theory in order to emphasize the degree of applicability of abstract compactness methods. Special attention is paid to multivalued perturbations of m-accretive operators; this case is analyzed under appropriate assumptions in order to allow the use of the general results in the study of some specific problems of great practical interest: reaction-diffusion and closed loop systems. Some biographical comments and open problems are also included. This new edition contains a number of improvements, corrections and insertions which both simplify and update the material. The book will be of interest to graduate students and specialists working in abstract evolution equations, partial differential equations, reaction-diffusion systems and ill-posed problems. A knowledge of topology, functional analysis and ordinary differential equations to undergraduate level is assumed.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 344

Добавлена в каталог: 28.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\breve{S}$mulian      6
Adams      12 298 309
Aizicovici      306 309
Alaoglu      7
Ames      37 309
Arino      6 7 8 301 305 309
Aris      146 309
Arrhenius      146
Arzela      1 10 57 62 63 64 83 86 89 168
Ascoli      1 10 57 62 63 64 83 86 89 168
Attouch      142 143 301 309
Aubin      301 310
Badii      300 305 310
Ball      39 40 298 310
Banach      16 44
Banach space, uniformly convex      18
Baras      64 299 300 310
Barbu      13 17 18 21 26 27 28 29 30 35 38 41 44 58 113 160 174 186 296 298 299 301 310
Bellman      3 134 194 237 238 271 279 282
Benilan      25 34 35 37 41 298 299 311
Bensoussan      308 311
Berens      256 312
Biroli      306 311
Boltzmann      24
Bounded domain with smooth boundary      12
Bourbaki      7
Brezis, D.      256 306 311
Brezis, H.      22 23 41 42 45 53 54 57 186 293 298 299 311
Browder      39 144 180 299 312
Buniakowsky      2 226
Butzer      256 312
Carath$\acute{e}$odory      134 135 136 141 142 143 152 161 178 179 180 181 182 186 191 305
Castaing      301 312
Cauchy      2 90 118 181 201 226 234 236 237 249 253
Cellina      301 310
Cioranescu      18 298 312
Clarkson      18
Crandall      30 34 38 298 299 306 311 312 313
Damlamian      142 143 301 309
Deimling      16 298 313
Diaz      300 301 305 310 313
Diestel      8 11 298 313
Dirichlet      23 105 256
Discretization ($\varepsilon$)      33
Dunford      1 11 321
Eberlein      6
Edwards      6 8 10 11 298 313
Effective domain      26
Egoroff      291
Evans      34 298 312
Fatou      28 77 109 114
Fermat      22
Fitzgibbon      307 313
FOURIER      51
Fujita      263 306 313
Function, $\phi$-demiclosed      199
Function, A-demiclosed      272
Function, A-dominated      272
Function, compact type, of      57
Function, conjugate      28
Function, convex      25
Function, indicator      27
Function, Lipschitz on bounded subsets      43
Function, lower semicontinuous (l. s. c.)      13
Function, proper      25
Function, upper semicontinuous (u. s. c.)      13
Gautier      6 7 8 301 305 309
Generalized directional derivative      43
Generalized gradient      44
Goursat      308 311
Green      22 23 97 249 251
Gripenberg      306 313
Gronwall      3
Gutman      12 79 82 300 301 314
H$\ddot{o}$lder      2 11 210 211 239
Hahn      16 44
Hale      307 314
Hardy      3 220 224 226 298 314
Hassan      300 310
Hazan      308 315
Hille      5 7 8 298 299 301 314
Hirano      300 314
Inequality, Bellman      3
Inequality, Buniakowsky — Schwarz      2
Inequality, Cauchy with e      2
Inequality, Gronwall      3
Inequality, H$\ddot{o}$lder      2
Inequality, Hardy      3
Inequality, Minkowski      2
Inequality, Tartar      2
Intermediate interpolation class      214
Kakutani      7
Kato      18 298 306 313 314
Kobayashi      34 298 314
Kolmogorov      1 11
Kondrashov      1 12
Konishi      57 299 314
Krein      308 315
Kuratowski      116 301 315
Ky Fan      308
Ladyzhenskaja      306 315
Lakshmikantham      14 15 34 35 2 98 315
Lasota      144 301 315
Lax      299
Lebesgue      77 93 179 286
Leeia      14 15 34 35 298 315
Lewis      146
Liggett      30 38 298 312
Lions      308 311
Littlewood      3 298 314
Local existence property      125
Londen      306 313
Luzin      291
Mapping, bounded      121
Mapping, compact      163
Mapping, continuous      118
Mapping, duality      16
Mapping, k-radial truncate of a      153
Mapping, local integrability property (having)      127
Mapping, measurable      116
Mapping, p — Carath$\acute{e}$odory      134
Mapping, positively sublinear      130
Mapping, superposition      148
Mapping, weakly continuous      118
Mapping, weakly p — Carath$\acute{e}$odory      134
Martin      298 302 305 315
Mazur      5 8 302
Maz’ya      12 315
Milman      18
Minkowski      2 94 281
Minty      26
Mitidieri      300 306 307 315
Moreau      26
Morimoto      263 313
Nagumo      305
Navier      195 256 306
Neumann      24 256
Nohel      306 313
Operator, accretive      19
Operator, compact      49
Operator, m-accretive      21
Operator, resolvent      20
Operator, superposition on $L^p(\Omega)$      91
Operator, superposition, or natural realization      25
Operator, well defined on $C(\overline{\Omega})$      91
Operator, well defined on $L^p(\Omega)$      91
Operator, Yosida approximation      20
Opial      144 301 315 322
Otani      305 306 316
P$\acute{o}$lya      3 298 314
Pavel      15 17 20 298 299 301 305 316
Pazy      39 43 53 55 85 144 180 256 298 299 300 305 306 311 316
Penot      6 7 8 301 305 309
Pettis      1 7 11 301
Phillips      5 7 8 298 299 301 314
Pierre      302 317
Plant      49 317
Popescu      300 317
Prater      146
Precupanu      13 29 58 298 310
Rellich      1 12
Riesz      1 11
Ryll — Nardzewski      116 301 315
Sato      15 16 317
Schauder      8 268 287 308
Schechter      302 317
Schiaffino      305 317
Schwarz      2 226
Selection      116
Semi-inner product, lower      14
Semi-inner product, normalized lower      14
Semi-inner product, normalized upper      14
Semi-inner product, upper      14
Semigroup, compact      50
Semigroup, equicontinuous      52
Semigroup, generated by -A      38
Semigroup, locally weakly equicontinuous      84
Semigroup, nonexpansive mappings, of      37
Semigroup, weakly equicontinuous      52
Set, compact      5
Set, equicontinuous      9
Set, p-equiintegrable      11
Set, precompact      5
Set, relatively compact      5
Set, relatively sequentially compact      5
Set, sequentially compact      5
Set, uniformly integrable      10
Set, weakly equicontinuous      9
Sobolev      112 247 250
Solution, generalized      30
Solution, integral      32
Solution, mild      34 124 265 283
Solution, mild in the sense of Browder      39
Solution, noncontinuable      125 232 2 70
Solution, p-approximate      136
Solution, strong      29 125 150 265 284
Solution, weak in the sense of Ball      39
Stefan      24 101
Stokes      195 256 306
Subdifferential      26
Tartar      2 105 192
Temam      306 318
Tesei      300 305 310
Thiele      146
Topology, strong      4
Topology, weak      4
Topology, weak star      4
Travis      307 318
Tychonoff      8 308
Uhl      8 11 298 313
Valadier      301 312
Veron      43 299 300 310 318
Vescan      308 318
Vitali      93 94
Volterra      71 264 265 272
Von Wahl      260 263 306 318
Vrabie      299 300 301 302 305 306 307 308 313 315 316 318
Vulikh      93 291 320
Webb      307 318
Weil      1 11
Yosida      5 7 18 20 45 298 320
Z$\breve{a}$linescu      18 320
Zorn      126 127 233 323
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