Fuchs M., Seregin G. — Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids :: Электронная библиотека попечительского совета мехмата МГУ

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Fuchs M., Seregin G. — Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

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Название: Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Авторы: Fuchs M., Seregin G.

Аннотация:

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2000

Количество страниц: 269

Добавлена в каталог: 15.08.2008

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Предметный указатель

$BD(\Omega; \mathbb{R}^{n})$       116
$D^{p, q}(\Omega)$       28 111
$D^{p, q}_{0}(\Omega)$ , $\bar{D}^{p, q}_{0}(\Omega)$       112
$D^{r}_{L ln L}(\Omega)$ , $\r{D}^{r}_{L ln L}(\Omega)$       251
$Exp(\Omega)$       212
$L ln L(\Omega)$       211
$V(\Omega)$ , $\r{V}(\Omega)$       213
$V^{p, q}_{0}(\Omega)$       112
$V_{0}(\Omega)$ , $\r{V}_{0}(\Omega)$       213
$X(\Omega)$ , $X_{loc}(\Omega)$ , $X_{0}(\Omega)$       237
Admissible stress tensor      8
Arcela's theorem      236
Banach space      101 254
Bingham fluid      132 136
Bingham variational inequality      193
Blow-up equation      147
Blow-up lemma      144
Bounded measure      33
Caccioppoli inequality      170
Caccioppoli-type estimate      57 65 216
Campanato-type estimate      138 163 204 229 245
Cauchy stress tensor      216
Coercivity      18 44
Conjugate function      9 16 42 248
Constitutive equations      7
Constitutive relations      248
Convexity      34 161
Deformation relations      7
Deformation theory      5 40 42 100
Difference quotient      259
Dirichlet boundary condition      134
Dirichlet-growth theorem      190
Dissipative potential      132 135
DOM      18
Duality      15
Egorov's theorem      149
Elastic domain      104 105
Elastic zone      45 51
Elasto-plastic boundary      105
Equilibrium equations for the stresses      7 43
Euler — Lagrange equation      147
Fatou's lemma      83
Finite difference method      57
Function of bounded deformation      33
Generalized Newtonian fluid      131—133
Haar — Karman principle      9
Hahn — Banach theorem      24
Hausdorff $\varphi$ -measure      98
Hausdorff dimension      98
Hausdorff measure      180
Hencky — Il'yushin plasticity      7 14 27 37 51
Hilbert space      254
Hoelder continuity      133 208 257
Hoelder continuous      97
Hoelder's inequality      140 256
Hole-filling trick      98
Imbedding theorem      111
Imbedding, compact      124
Imbedding, continuous      124
Int dom      18
Jensen's inequality      55 91 126
Kinematically admissible displacement      8
Korn type inequality      133
Korn's inequality      75 137 139 141 163
Korn's inequality, $L^{p}$       111
Lagrange's formula      89
Lagrangian      8 9 15 27
Lebesgue measure      56 98
Lebesgue point      143 161 256
Lebesgue space      8 255

Lebesgue's theorem      83
Legendre transformation      37 49 104
Linear elasticity      51 104
Linear hardening      101
Logarithmic hardening      207 209 237
Lower semicontinuity      161
Maximal function      211
Mean oscillation      257
Minimax problem      8 10 23 27 28 33
Minimizing sequence      24
Morrey space      143 198
N-function      248 249
Navier — Stokes system      135
Newton fluid      136
Non reflexive space      15
Nonlinear system of Stokes type      204
Normed dual      254
Norton fluid      136
Orlicz — Sobolev space      248
p-Bingham variational inequality      204
Partial regularity      50
Perfect elastoplasticity      5
Perturbed functional      16
Plastic deformation      105
Plastic domain      104 105
Plastic zone      45
Plasticity with hardening      14
Plasticity with power hardening      100
Poincare's inequality      259
Powell — Eyring model      136
Prandtl — Eyring fluid      136 208 211
Prandtl — Eyring model      136
Precompactness      124
Quasi-static case      132
Quasi-static fluid      131
Radon measure      55 116
Reflexive space      18 102 255
Relaxation      15 33
Relaxed Lagrangian      33
Relaxed minimax problem      44
Rigid body      133
Rigid zone      192
Saddle point      10 24
Safe load condition      10 30 35 44
Smoothing kernel      108
Sobolev space      8 257
Sobolev — Poincare inequality      259
Sobolev's imbedding theorem      258
Sobolev's inequality      74
Solenoidal vector field      115
Solenoidal vector-valued function      110
Star-shaped domain      117
Stationary case      132
Steady state motion      132
Stokes system      134 138
Stress deviator      132
Subdifferential      132
Superlinear growth      101
Sutterby fluid model      249
Taylor's formula      81
Trace      258
Upper semicontinuity      54
Viscoplastic fluid      132
Von Mises yield condition      7
Weak convergence      254
Weak limit      254
Weak lower semicontinuity      254
Weak solution      5 27
Weak- $\ast$ topology      54
Yield surface      7
Young's inequality      63 140 256

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