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Showalter R.E. — Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
Showalter R.E. — Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

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Название: Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

Автор: Showalter R.E.

Аннотация:

A monograph presenting topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial- boundary-value problems for partial differential equations and to construct such operators as realizations for those problems in appropriate function spaces. For advanced graduate students, research mathematicians, and engineers interested in numerical analysis, applied mathematics, control theory, or dynamical systems.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 278

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^0$ solution      233 237 218
$H^{-1}$-solution      143
$\varepsilon$-solution      218
A-priori estimate      43 166 170
Absolutely continuous      104
Abstract Green's Theorem      64 87 165 193
Accretive, m-accretive      18 158 211 212 221
Adjoint      18 37
Adjoint form      19
Adler problem      63
Affine function      80
Angle condition      9
Annihilator      64
Approximate      172
Approximate equations      213
Backward parabolic      119
Banach space      3 35
Barrel      79
Bidual      35
Boundary condition      165
Boundary control      199
Boundary hysteresis      238 249
Boundary operator      64 87 193
Boundary values      54
Bounded      36 59
Bounded linear functions      7
Caratheodory conditions      48
Cauchy problem      22 107 108 111 114 120 129 136 150 168 171 201 208 209 228
Cauchy sequence      6
cells      255
Chain rule      82 186
Closed      8 17 36
Coercive      2 38 170
Compact      36 106
Comparison estimates      98
Compatibility      145 195
Compatibility condition      197 199
complete      6
completely continuous      36 40
Composite material      249
Compressibility      254
Conductivity      244
Cone      15 70
Cone condition      58
conjugate      204
Conservation of energy      241
Conservation of fluid      253
Constitutive equation      257
continuous      2 7 36 59 234
Continuous dependence      229
Contraction      9
Convex      8 78 144 156
Coordinate patch      56
Darcy's law      253
Degenerate      235 243
Demicontinuous      36
density      253
Derivative      8
Different iable      162
Dirac functional      3
Directional derivative      80 220
Dirichlet boundary condition      194 242 249
Dirichlet problem      1 19 59 62 93
Displacement      256
Displacement rate      256
Distributed microstructure model      252
distribution      2
Domain      17 156 158
Double porosity model      255
Doubly-nonlinear      167 169
Dual      8 37 138
Dual space      35
Duality map      91
Dynamic boundary condition      140 238 249
Dynamic models      246
Effective domain      78
Elastic      72 152 257
Elliptic      10 109 216
Elliptic equation in the tangent space      68
Elliptic-parabolic      117
Elongation      257
Elongation rate      257
Energy      88
Energy estimate      114 176 187
entropy      234
Epigraph      78 156
Equation of state      253
Equicontinuous      50
Equivalent scalar product      10
Essentially bounded      44
Exact      157
Existence      145 213 226
Exponential shift      112
Extension      57
Fast diffusion      254
Finite-difference      127
First order kinetic models      235 250
First type      62 140
Fissured medium equation      250
Fissures      255
Flat      67
Flux      242 253
Formal operator      64 193
Formal part      65 87
Fourier's law      241
Fourth type      63 140
Free boundary      245
Free surface      72
Free-boundary problem      16
G-differential      80
Gauge      91
Generalized derivative      1 52
Generalized functions      51
Generalized play      246
Generalized porous medium equation      254
Generalized solution      183
Generator      23
Gradient      162
Graph      17 243 253
Graph-convergent      229
Green's formula      64
Gronwall inequalities      179
Group      26
heat capacity      241
Heat equation      241 258
Heat flux      241
Heat recuperator      252
Heaviside function      3
Heaviside functional      3
Heaviside graph      89 244 246
Hemicontinuous      37
history      237 246
History-value problem      131 150 188
Hyperplane      80
Hysteresis      237 246 261
Imbedding      45
Implicit evolution equations      134
Indicator function      78 261
Initial data      137
Initial-boundary-value problem      110
Initial-value problem      21 107
Integrable      103
Interface conditions      242
Interior-coupled      67
Internal energy      243
Interpolation      45
Invariance property      148
Inverse      158
Latent heat      243
Left derivative      220
Linear      36
Linear contraction semigroup      22
Locally bounded      39
Locally integrable      2
Lower-semi-continuous      156
Manifold      56
Maximal accretive      159
Maximal monotone      39
Maximum principle      148
Measurable      103
Metric      6
Minimal section      161
Minimization principle      8
Mixed type      63
Mollifler      46
Momentum equation      257
Monotone      9 22 37 60 69 201
Monotone, weakly continuous      40
Multi-valued      78
Negative part      96
Nemytskii operators      49
Neumann boundary condition      126 238 242 249
Neumann problem      1 20 62
Neumann type      194
Newton's law      242
Non-cyclindrical      110
Non-local      63 134
Norm      6
Norm convergence      35
normal      80
Normalized duality map      91
Orthogonal      9
Orthogonal complement      9
Parabolic regularizing property      28
Parabolic systems      133
Parabolic variational inequalities      144
Parallel flow      249
Parallel flow model      235 249
Partial saturation      253
Partition-of-unity      53 56
Periodic      181
Periodic Problem      112 131 150 215
Periodic semigroup      131
Permeability      253
Perturbation      195
Phase      243 247
Pivot space      64 138
Plastic      72 152 261
Porosity      253
Porous medium equation      101 142 204 234 235 243 254
Positive part      94 100 233
Positive sign      89
potential energy      13
Prandtl      261
Precompact      36
Pressure      253
Projection      9
Proper      78 156
Pseudo-monotone operators      40 41
Pseudoparabolic      235
Quasilinear      61
Quasilinear diffusion equation      260
Quasilinear parabolic      125
Quasilinear parabolic problem      198
Quasilinear porous medium equation      254
Quasilinear wave equation      260
Quasilinear-damped wave equation      260
Quasimonotone      40 69
RANGE      158
Rate estimate      187
Reflexive      35
Regular      113 115
Regular accretive      22 191
Regular distributions      3
Regular m-accretive      22
Regular pair      207
Regularity      114 129 145 147 195 203
Regularization      224
Regularize      99 172
Regularizing effects      28 258
Regularizing property      175 176 185 195
Regularizing sequence      46
Relation      157 211 78 243
Relay hysteresis      247
Resistance      253
Resolvent      17 159 239
retract      37
Reversible      33 194
Riesz map      10 91
Robin boundary condition      126 242
Robin problem      62
Saltus      244
Scalar conservation law      101 233
Scalar product      6
Second dual      35
Second type      62 140
Second-order evolution equations      207
Segment property      54
Self-adjoint      28
Semigroup of contractions      176
Semigroup of translations      127
Semilinear      243
Semilinear evolution equations      216
Semilinear parabolic      217
Separable      155
Separates      156
Sign function      14 47 247
Sign graph      261
Signal speed      234
Signorini conditions      237
Signorini problem      70
Simple play      238
singular      235 243
Singular Cauchy problem      131 132
Singular evolution equation      132
Singular-in-time      188
Slightly compressible      254
Slow diffusion      254
Sobolev space      6 52
Solution      171 201 208 209 210
Source density      253
Spatial regularity      29
Specific heat      241 243 244
Stable boundary conditions      62
Stefan Problem      244 235
Stefan system      251
strain      257
Stress      256 257
Strict contraction      166
Strictly convex      90
Strictly monotone      39
Strong convergence      35
Strong derivative      53
Strong problem      144
Strong solution      108 123 128 153 154 219
Strongly monotone      39
Strongly singular      188
Strongly-accretive      169
Subdifferentiable      81
Subdifferential      81
Subgradient      78 157
Super-Stefan problem      248
Support      2 46
system      73 255
Tangential coordinates      67
Temporal regularity      29
Test functions      2 46 51
Thermoelasticity      265
Third type      62 140
Trace      54 164 193
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