Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel ; Boston ; Berlin
Birkhäuser
2000
|
| Schriftenreihe: | Operator theory
119 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 522 S. |
| ISBN: | 3764361999 |
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| 100 | 1 | |a Litvinov, Vil'iam G. |d 1934- |e Verfasser |0 (DE-588)121954730 |4 aut | |
| 245 | 1 | 0 | |a Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |c William G. Litvinov |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 2000 | |
| 300 | |a XXII, 522 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 119 | |
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Operator theory |v 119 |w (DE-604)BV000000970 |9 119 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008961723&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805068453079416832 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
XV
INTRODUCTION
.
XIX
1
BASIC
DEFINITIONS
AND
AUXILIARY
STATEMENTS
1.1
SETS,
FUNCTIONS,
REAL
NUMBERS
.
1
1.1.
T
NOTATIONS
AND
DEFINITIONS
.
1
1.1.2
REAL
NUMBERS
.
2
1.2
TOPOLOGICAL,
METRIC,
AND
NORMED
SPACES
.
4
1.2.1
GENERAL
NOTIONS
.
4
1.2.2
METRIC
SPACES
.
5
1.2.3
NORMED
VECTOR
SPACES
.
.'
6
1.3
CONTINUOUS
FUNCTIONS
AND
COMPACT
SPACES
.
10
1.3.1
CONTINUOUS
AND
SEMICONTINUOUS
MAPPINGS
.
10
1.3.2
COMPACT
SPACES
.
12
1.3.3
CONTINUOUS
FUNCTIONS
ON
COMPACT
SPACES
.
13
1.4
MAXIMUM
FUNCTION
AND
ITS
PROPERTIES
.
14
1.4.1
DISCRETE
MAXIMUM
FUNCTION
.
14
1.4.2
GENERAL
MAXIMUM
FUNCTION
.
16
1.5
HILBERT
SPACE
.
17
1.5.1
BASIC
DEFINITIONS
AND
PROPERTIES
.
17
1.5.2
COMPACT
AND
SELFADJOINT
OPERATORS
IN
A
HILBERT
SPACE
.
20
1.5.3
THEOREM
ON
CONTINUITY
OF
A
SPECTRUM
.
25
1.5.4
EMBEDDING
OF
A
HILBERT
SPACE
IN
ITS
DUAL
.
31
1.5.5
SCALES
OF
HILBERT
SPACES
AND
COMPACT
EMBEDDING
.
33
1.6
FUNCTIONAL
SPACES
THAT
ARE
USED
IN
THE
INVESTIGATION
OF
BOUNDARY
VALUE
AND
OPTIMAL
CONTROL
PROBLEMS
.
36
1.6.1
SPACES
OF
CONTINUOUSLY
DIFFERENTIABLE
FUNCTIONS
.
36
1.6.2
SPACES
OF
INTEGRABLE
FUNCTIONS
.
37
1.6.3
TEST
AND
GENERALIZED
FUNCTIONS
.
37
1.6.4
SOBOLEV
SPACES
.
39
1.7
INEQUALITIES
OF
COERCIVENESS
.
44
1.7.1
COERCIVE
SYSTEMS
OF
OPERATORS
.
44
1.7.2
KORN
'
S
INEQUALITY
.
48
VIII
CONTENTS
1.8
THEOREM
ON
THE
CONTINUITY
OF
SOLUTIONS
OF
FUNCTIONAL
EQUATIONS
.
50
1.9
DIFFERENTIATION
IN
BANACH
SPACES
AND
THE
IMPLICIT
FUNCTION
THEOREM
.
51
1.9.1
FRECHET
DERIVATIVE
AND
ITS
PROPERTIES
.
51
1.9.2
IMPLICIT
FUNCTION
.
52
1.9.3
THE
GATEAUX
DERIVATIVE
AND
ITS
CONNECTION
WITH
THE
FRECHET
DERIVATIVE
.
53
1.10
DIFFERENTIATION
OF
THE
NORM
IN
THE
SPACE
WYY(Q)
.
54
1.10.1
AUXILIARY
STATEMENT
.
54
1.10.2
THEOREM
ON
DIFFERENTIABILITY
.
55
1.11
DIFFERENTIATION
OF
EIGENVALUES
.
58
1.11.1
THE
EIGENVALUE
PROBLEM
.
58
1.11.2
DIFFERENTIATION
OF
AN
OPERATOR-VALUED
FUNCTION
.
60
1.11.3
EIGENSPACES
AND
PROJECTIONS
.
61
1.11.4
DIFFERENTIATION
OF
EIGENVALUES
.
64
1.12
THE
LAGRANGE
PRINCIPLE
IN
SMOOTH
EXTREMUM
PROBLEMS
.
70
1.13
G-CONVERGENCE
AND
G-CLOSEDNESS
OF
LINEAR
OPERATORS
.
72
1.14
DIFFEOMORPHISMS
AND
INVARIANCE
OF
SOBOLEV
SPACES
WITH
RESPECT
TO
DIFFEOMORPHISMS
.
73
1.14.1
DIFFEOMORPHISMS
AND
THE
RELATIONS
BETWEEN
THE
DERIVATIVES
.
73
1.14.2
SEQUENTIAL
FRECHET
DERIVATIVES
AND
PARTIAL
DERIVATIVES
OF
A
COMPOSITE
FUNCTION
.
75
1.14.3
THEOREM
ON
THE
INVARIANCE
OF
SOBOLEV
SPACES
.
76
1.14.4
TRANSFORMATION
OF
DERIVATIVES
UNDER
'
S
THE
CHANGE
OF
VARIABLES
.
78
2
OPTIMAL
CONTROL
BY
COEFFICIENTS
IN
ELLIPTIC
SYSTEMS
2.1
DIRECT
PROBLEM
.
81
2.1.1
COERCIVE
FORMS
AND
OPERATORS
.
81
2.1.2
BOUNDARY
VALUE
PROBLEM
.
82
2.2
OPTIMAL
CONTROL
PROBLEM
.
86
2.2.1
NONREGULAR
CONTROL
.
86
2.2.2
REGULAR
CONTROL
.
88
2.2.3
REGULAR
PROBLEM
AND
NECESSARY
CONDITIONS
OF
OPTIMALITY
.
90
2.2.4
NONSMOOTH
(DISCONTINUOUS)
CONTROL
.
97
2.2.5
SOME
REMARKS
ON
THE
USE
OF
REGULAR
AND
DISCONTINUOUS
CONTROLS
.
102
2.3
THE
FINITE-DIMENSIONAL
PROBLEM
.
103
CONTENTS
IX
2.4
THE
FINITE-DIMENSIONAL
PROBLEM
(ANOTHER
APPROACH)
.
105
2.4.1
THE
SET
U&
.
105
2.4.2
APPROXIMATE
SOLUTION
OF
THE
PROBLEM
(2.2.22)
.
107
2.4.3
APPROXIMATE
SOLUTION
OF
THE
OPTIMAL
CONTROL
PROBLEM
O
WHEN
THE
SET
C7
A
D
IS
EMPTY
.
109
2.4.4
ON
THE
COMPUTATION
OF
THE
FUNCTIONAL
H
-
.
110
2.4.5
CALCULATION
AND
USE
OF
THE
FRECHET
DERIVATIVE
OF
THE
FUNCTIONAL
H
-
+
^
RN
(H,
UH
)
.
113
2.5
SPECTRAL
PROBLEM
.
117
2.5.1
EIGENVALUE
PROBLEM
.
117
2.5.2
ON
THE
CONTINUITY
OF
THE
SPECTRUM
.
118
2.6
OPTIMIZATION
OF
THE
SPECTRUM
.
120
2.6.1
FORMULATION
OF
THE
PROBLEM
AND
THE
EXISTENCE
THEOREM
.
120
2.6.2
FINITE-DIMENSIONAL
APPROXIMATION
OF
THE
OPTIMAL
CONTROL
PROBLEM
.
122
2.6.3
COMPUTATION
OF
EIGENVALUES
.
127
2.7
CONTROL
UNDER
RESTRICTIONS
ON
THE
SPECTRUM
.
129
2.7.1
OPTIMAL
CONTROL
PROBLEM
.
129
2.7.2
APPROXIMATE
SOLUTION
OF
THE
PROBLEM
(2.7.7)
.
131
2.7.3
SECOND
METHOD
OF
APPROXIMATE
SOLUTION
OF
THE
PROBLEM
(2.7.7)
.
132
2.7.4
DIFFERENTIATION
OF
THE
FUNCTIONALS
H
-
AJ/Z(/I)
AND
NECESSARY
CONDITIONS
OF
OPTIMALITY
.
135
2.8
THE
BASIC
OPTIMAL
CONTROL
PROBLEM
.
138
2.8.1
SETTING
OF
THE
PROBLEM.
EXISTENCE
THEOREM
.
138
2.8.2
APPROXIMATE
SOLUTION
OF
THE
PROBLEM
(2.8.6)
.
140
2.9
THE
COMBINED
PROBLEM
.
142
2.10
OPTIMAL
CONTROL
PROBLEM
FOR
THE
CASE
WHEN
THE
STATE
OF
THE
SYSTEM
IS
CHARACTERIZED
BY
A
SET
OF
FUNCTIONS
.
145
2.10.1
SETTING
OF
THE
PROBLEM
.
145
2.10.2
THE
EXISTENCE
THEOREM
.
146
2.11
THE
GENERAL
CONTROL
PROBLEM
.
149
2.11.1
BILINEAR
FORM
A
Q
AND
THE
CORRESPONDING
EQUATION
.
150
2.11.2
BILINEAR
FORM
B
R
AND
THE
SPECTRAL
PROBLEM
.
153
2.11.3
BASIC
CONTROL
PROBLEM
.
154
2.11.4
APPLICATION
OF
THE
BASIC
CONTROL
PROBLEM
(COMBINED
PROBLEM)
.
157
2.12
OPTIMIZATION
BY
THE
SHAPE
OF
DOMAIN
AND
BY
OPERATORS
.
159
2.12.1
DOMAINS
AND
BILINEAR
FORMS
.
159
X
CONTENTS
2.12.2
OPTIMIZATION
PROBLEM
CONNECTED
WITH
SOLUTION
OF
AN
OPERATOR
EQUATION
.
160
2.12.3
EIGENVALUE
OPTIMIZATION
PROBLEM
.
162
2.12.4
SOME
REALIZATIONS
OF
THE
SPACES
MI
AND
NI
.
164
2.13
OPTIMIZATION
PROBLEMS
WITH
SMOOTH
SOLUTIONS
OF
STATE
EQUATIONS
.
168
2.13.1
SYSTEMS
OF
ELLIPTIC
EQUATIONS
.
168
2.13.2
ELLIPTIC
PROBLEMS
IN
DOMAINS
AND
IN
A
FIXED
DOMAIN
.
170
2.13.3
THE
PROBLEM
OF
DOMAIN
SHAPE
OPTIMIZATION
.
173
2.13.4
APPROXIMATE
SOLUTION
OF
THE
DIRECT
PROBLEM
ENSURING
CONVERGENCE
IN
THE
NORM
OF
A
SPACE
OF
SMOOTH
FUNCTIONS
.
174
3
CONTROL
BY
THE
RIGHT-HAND
SIDES
IN
ELLIPTIC
PROBLEMS
3.1
ON
THE
MINIMUM
OF
NONLINEAR
FUNCTIONALS
.
177
3.1.1
SETTING
OF
THE
PROBLEM.
AUXILIARY
STATEMENTS
.
177
3.1.2
THE
EXISTENCE
THEOREM
.
179
3.1.3
CHARACTERIZATION
OF
A
MINIMIZING
ELEMENT
.
181
3.1.4
FUNCTIONALS
CONTINUOUS
IN
THE
WEAK
TOPOLOGY
.
182
3.2
APPROXIMATE
SOLUTION
OF
THE
MINIMIZATION
PROBLEM
.
183
3.2.1
INNER
POINT
LEMMA
.
183
3.2.2
FINITE-DIMENSIONAL
PROBLEM
.
185
3.3
CONTROL
BY
THE
RIGHT-HAND
SIDE
IN
ELLIPTIC
PROBLEMS
PROVIDED
THE
GOAL
FUNCTIONAL
IS
QUADRATIC
.
191
3.3.1
SETTING
OF
THE
PROBLEM
.
191
3.3.2
EXISTENCE
OF
A
SOLUTION.
OPTIMALITY
CONDITIONS
.
192
3.3.3
AN
EXAMPLE
OF
A
SYSTEM
DESCRIBED
BY
THE
DIRICHLET
PROBLEM
.
194
3.4
MINIMAX
CONTROL
PROBLEMS
.
198
3.5
CONTROL
OF
SYSTEMS
WHOSE
STATE
IS
DESCRIBED
BY
VARIATIONAL
INEQUALITIES
.
201
3.5.1
SETTING
OF
THE
PROBLEM
.
201
3.5.2
THE
EXISTENCE
THEOREM
.
203
3.5.3
AN
EXAMPLE
OF
CONTROL
OF
A
SYSTEM
DESCRIBED
BY
A
VARIATIONAL
INEQUALITY
.
205
4
DIRECT
PROBLEMS
FOR
PLATES
AND
SHELLS
4.1
BENDING
AND
FREE
OSCILLATIONS
OF
THIN
PLATES
.
209
4.1.1
BASIC
RELATIONS
OF
THE
THEORY
OF
BENDING
OF
THIN
PLATES
.
209
4.1.2
ORTHOTROPIC
PLATES
.
211
4.1.3
BILINEAR
FORM
CORRESPONDING
TO
THE
STRAIN
ENERGY
OF
THE
PLATE
.
212
4.1.4
PROBLEM
OF
BENDING
OF
A
PLATE
.
215
CONTENTS
XI
4.1.5
PROBLEM
OF
FREE
OSCILLATIONS
OF
A
PLATE
.
221
4.2
PROBLEM
OF
STABILITY
OF
A
THIN
PLATE
.
223
4.2.1
STORED
ENERGY
OF
A
PLATE
.
223
4.2.2
CONDITIONS
OF
STATIONARITY
.
226
4.2.3
AUXILIARY
STATEMENTS
.
228
4.2.4
TRANSFORMATION
OF
THE
PROBLEM
(4.2.27),
(4.2.28)
.
231
4.2.5
STABILITY
OF
A
PLATE
AND
BIFURCATION
.
235
4.2.6
AN
EXAMPLE
OF
NONEXISTENCE
OF
STABLE
SOLUTIONS
.
239
4.3
MODEL
OF
THE
THREE-LAYERED
PLATE
IGNORING
SHEARS
IN
THE
MIDDLE
LAYER
.
242
4.3.1
BASIC
RELATIONS
.
242
4.3.2
PROBLEMS
OF
THE
BENDING
AND
OF
THE
FREE
FLEXURAL
OSCILLATIONS
.
244
4.4
MODEL
OF
THE
THREE-LAYERED
PLATE
ACCOUNTING
FOR
SHEARS
IN
THE
MIDDLE
LAYER
.
246
4.4.1
BASIC
RELATIONS
.
246
4.4.2
BILINEAR
FORM
CORRESPONDING
TO
THE
THREE-LAYERED
PLATE
.
250
4.4.3
BENDING
OF
THE
THREE-LAYERED
PLATE
.
253
4.4.4
NATURAL
OSCILLATIONS
OF
THREE-LAYERED
PLATE
.
255
4.5
BASIC
RELATIONS
OF
THE
SHELL
THEORY
.
257
4.6
SHELLS
OF
REVOLUTION
.
260
4.6.1
DEFORMATIONS
AND
FUNCTIONAL
SPACES
.
260
4.6.2
THE
BILINEAR
FORM
AH
.
262
4.6.3
THE
SUBSPACE
OF
FUNCTIONS
WITH
ZERO-POINT
STRAIN
ENERGY
.
264
4.7
SHALLOW
SHELLS
.
265
4.8
PROBLEMS
OF
STATICS
OF
SHELLS
.
267
4.9
FREE
OSCILLATIONS
OF
A
SHELL
.
268
4.10
PROBLEM
OF
SHELL
STABILITY
.
270
4.10.1
ON
SOME
APPROACHES
TO
STABILITY
PROBLEMS
.
270
4.10.2
REDUCING
OF
THE
STABILITY
PROBLEM
TO
THE
EIGENVALUE
PROBLEM
.
271
4.10.3
SPECTRAL
PROBLEM
(4.10.12)
.
272
4.11
FINITE
SHEAR
MODEL
OF
A
SHELL
.
274
4.11.1
STRAIN
ENERGY
OF
AN
ELASTIC
SHELL
.
274
4.11.2
SHALLOW
SHELL
.
276
4.11.3
A
RELATION
BETWEEN
THE
KIRCHHOFF
AND
TIMOSHENKO
MODELS
OF
SHELL
.
278
4.12
LAMINATED
SHELLS
.
282
4.12.1
THE
STRAIN
ENERGY
OF
A
LAMINATED
SHELL
.
282
4.12.2
SHELL
OF
REVOLUTION
.
284
4.12.3
SHALLOW
SHELLS
.
286
XII
CONTENTS
5
OPTIMIZATION
OF
DEFORMABLE
SOLIDS
5.1
SETTINGS
OF
OPTIMIZATION
PROBLEMS
FOR
PLATES
AND
SHELLS
.
287
5.1.1
GOAL
FUNCTIONAL
AND
A
FUNCTION
OF
CONTROL
.
287
5.1.2
RESTRICTIONS
.
289
5.2
APPROXIMATE
SOLUTION
OF
DIRECT
AND
OPTIMIZATION
PROBLEMS
FOR
PLATES
AND
SHELLS
.
291
5.2.1
DIRECT
PROBLEMS
AND
SPLINE
FUNCTIONS
.
291
5.2.2
THE
SPACES
V
M
FOR
PLATES
.
292
5.2.3
THE
SPACES
V
M
FOR
SHELLS
.
294
5.2.4
DIRECT
PROBLEMS
FOR
NONFASTENED
PLATES
AND
SHELLS
.
297
5.2.5
SOLUTION
OF
OPTIMIZATION
PROBLEMS
.
298
5.3
OPTIMIZATION
PROBLEMS
FOR
PLATES
(CONTROL
BY
THE
FUNCTION
OF
THE
THICKNESS)
.
300
5.3.1
OPTIMIZATION
UNDER
RESTRICTIONS
ON
STRENGTH
.
300
5.3.2
STABILITY
OPTIMIZATION
PROBLEM
.
305
5.3.3
OPTIMIZATION
OF
FREQUENCIES
OF
FREE
OSCILLATIONS
.
311
5.3.4
COMBINED
OPTIMIZATION
PROBLEM
AND
OPTIMIZATION
FOR
A
CLASS
OF
LOADS
.
312
5.4
OPTIMIZATION
PROBLEMS
FOR
SHELLS
(CONTROL
BY
FUNCTIONS
OF
MIDSURFACE
AND
THICKNESS)
.
312
5.4.1
PROBLEM
OF
OPTIMIZATION
OF
A
SHELL
OF
REVOLUTION
WITH
RESPECT
TO
STRENGTH
.
313
5.4.2
OPTIMIZATION
ACCORDING
TO
THE
STABILITY
OF
A
CYLINDRICAL
SHELL
SUBJECT
TO
A
HYDROSTATIC
COMPRESSIVE
LOAD
.
316
5.5
CONTROL
BY
THE
SHAPE
OF
A
HOLE
AND
BY
THE
FUNCTION
OF
THICKNESS
FOR
A
SHALLOW
SHELL
.
.
319
5.5.1
PROBLEM
OF
OPTIMIZATION
ACCORDING
TO
STRENGTH
.
319
5.5.2
APPROXIMATE
SOLUTION
OF
THE
OPTIMIZATION
AND
DIRECT
PROBLEMS
.
322
5.5.3
PROBLEM
OF
OPTIMIZATION
OF
EIGENVALUES
.
324
5.5.4
APPROXIMATE
SOLUTION
OF
THE
EIGENVALUE
PROBLEM
.
325
5.6
CONTROL
BY
THE
LOAD
FOR
PLATES
AND
SHELLS
.
326
5.6.1
GENERAL
PROBLEM
OF
CONTROL
BY
THE
LOAD
.
326
5.6.2
OPTIMIZATION
PROBLEMS
FOR
PLATES
.
327
5.7
OPTIMIZATION
OF
STRUCTURES
OF
COMPOSITE
MATERIALS
.
333
5.7.1
CONCEPT
OF
A
COMPOSITE
MATERIAL
.
333
5.7.2
HOMOGENIZATION
(AVERAGING)
OF
A
PERIODICAL
STRUCTURE
BASED
ON
G-CONVERGENCE
.
334
5.7.3
EFFECTIVE
ELASTICITY
CHARACTERISTICS
OF
GRANULE
AND
FIBER
REINFORCED
COMPOSITES
.
343
5.7.4
OPTIMIZATION
OF
THE
EFFECTIVE
ELASTICITY
CONSTANTS
OF
A
COMPOSITE
.
348
CONTENTS
XIII
5.7.5
OPTIMIZATION
OF
A
GRANULE
REINFORCED
COMPOSITE
.
354
5.7.6
OPTIMIZATION
OF
COMPOSITE
LAMINATE
SHELLS
.
357
5.7.7
OPTIMIZATION
OF
THE
COMPOSITE
STRUCTURE
.
367
5.8
OPTIMIZATION
OF
LAMINATE
COMPOSITE
COVERS
ACCORDING
TO
MECHANICAL
AND
RADIO
ENGINEERING
CHARACTERISTICS
.
373
5.8.1
PROPAGATION
OF
ELECTROMAGNETIC
WAVES
THROUGH
A
LAMINATED
MEDIUM
.
373
5.8.2
OPTIMIZATION
PROBLEMS
.
380
5.9
SHAPE
OPTIMIZATION
OF
A
TWO-DIMENSIONAL
ELASTIC
BODY
.
383
5.9.1
SETS
OF
CONTROLS
AND
DOMAINS
IN
THE
OPTIMIZATION
PROBLEM
383
5.9.2
PROBLEMS
OF
ELASTICITY
IN
DOMAINS
.
384
5.9.3
THE
OPTIMIZATION
PROBLEM
.
386
5.10
OPTIMIZATION
OF
THE
INTERNAL
BOUNDARY
OF
A
TWO-DIMENSIONAL
ELASTIC
BODY
.
388
5.11
OPTIMIZATION
PROBLEMS
ON
MANIFOLDS
AND
SHAPE
OPTIMIZATION
OF ELASTIC
SOLIDS
.
391
5.11.1
OPTIMIZATION
PROBLEM
FOR
AN
ELASTIC
SOLID
.
392
5.11.2
SPACES
AND
OPERATORS
ON
R/2
TT
Z,
AUXILIARY
STATEMENTS
.
398
5.11.3
OPTIMIZATION
PROBLEM
ON
R/2
TT
Z
.
405
5.12
OPTIMIZATION
OF
THE
RESIDUAL
STRESSES
IN
AN
ELASTOPLASTIC
BODY
.
409
5.12.1
FORCE
AND
THERMAL
LOADING
OF
A
NONLINEAR
ELASTOPLASTIC
BODY
.
410
5.12.2
RESIDUAL
STRESSES
AND
DEFORMATIONS
.
421
5.12.3
TEMPERATURE
PATTERN
IN
A
MEDIUM
.
424
5.12.4
OPTIMIZATION
PROBLEM
.
426
6
OPTIMIZATION
PROBLEMS
FOR
STEADY
FLOWS
OF
VISCOUS
AND
NONLINEAR
VISCOUS
FLUIDS
6.1
PROBLEM
OF
STEADY
FLOW
OF
A
NONLINEAR
VISCOUS
FLUID
.
431
6.1.1
BASIC
EQUATIONS
AND
ASSUMPTIONS
.
431
6.1.2
FORMULATION
OF
THE
PROBLEM
.
434
6.1.3
EXISTENCE
THEOREM
.
439
6.2
THEOREM
ON
CONTINUITY
.
443
6.3
CONTINUITY
WITH
RESPECT
TO
THE
SHAPE
OF
THE
DOMAIN
.
446
6.3.1
FORMULATION
OF
THE
PROBLEM
.
446
6.3.2
LEMMAS
ON
OPERATORS
L
Q
AND
B
Q
.
448
6.3.3
THEOREM
ON
CONTINUITY
.
451
6.4
CONTROL
OF
FLUID
FLOWS
BY
PERFORATED
WALLS
AND
COMPUTATION
OF
THE
FUNCTION
OF
FILTRATION
.
454
XIV
CONTENTS
6.4.1
THE
PROBLEM
OF
FLOW
IN
A
CIRCULAR
CYLINDER
AND
THE
FUNCTION
OF
FILTRATION
.
455
6.4.2
THE
PASSAGE
FACTOR
FOR
THE
POWER
MODEL
.
458
6.4.3
CONTROL
OF
THE
SURFACE
FORCES
AT
THE
INLET
BY
THE
PERFORATED
WALL
.
459
6.5
THE
FLOW
IN
A
CANAL
WITH
A
PERFORATED
WALL
PLACED
INSIDE
.
460
6.5.1
BASIC
EQUATIONS
.
460
6.5.2
GENERALIZED
SOLUTION
OF
THE
PROBLEM
.
462
6.6
OPTIMIZATION
BY
THE
FUNCTIONS
OF
SURFACE
FORCES
AND
FILTRATION
.
463
6.6.1
FORMULATION
OF
THE
PROBLEM
AND
THE
EXISTENCE
THEOREM
.
463
6.6.2
ON
THE
DIFFERENTIABILITY
OF
THE
FUNCTION
(U(T),P(T))
.
465
6.6.3
DIFFERENTIABILITY
OF
THE
FUNCTIONALS
AND
NECESSARY
OPTIMALITY
CONDITIONS
.
470
6.7
PROBLEMS
OF
THE
OPTIMAL
SHAPE
OF
A
CANAL
.
471
6.7.1
SET
OF
CONTROLS
AND
DIFFEOMORPHISMS
.
472
6.7.2
OPTIMIZATION
PROBLEMS
.
474
6.8
A
PROBLEM
OF
THE
OPTIMAL
SHAPE
OF
A
HYDROFOIL
.
478
6.8.1
STATE
EQUATION
FOR
A
MOVING
HYDROFOIL
.
478
6.8.2
FIXED-DOMAIN
PROBLEM
AND
FRECHET
DIFFERENTIABILITY
OF
THE
FUNCTIONALS
.
485
6.8.3
OPTIMIZATION
PROBLEM
.
493
6.9
DIRECT
AND
OPTIMIZATION
PROBLEMS
WITH
CONSIDERATION
FOR
THE
INERTIA
FORCES
.
495
6.9.1
SETTING
AND
SOLUTION
OF
THE
DIRECT
PROBLEM
.
.
.
495
6.9.2
APPROXIMATION
OF
THE
PROBLEM
(6.9.10)-(6.9.12)
.
500
6.9.3
SOME
REMARKS
ON
MODELS,
OPTIMIZATION
PROBLEMS,
AND
EXISTENCE
RESULTS
.
501
BIBLIOGRAPHY
.
503
INDEX
.
519 |
| any_adam_object | 1 |
| author | Litvinov, Vil'iam G. 1934- |
| author_GND | (DE-588)121954730 |
| author_facet | Litvinov, Vil'iam G. 1934- |
| author_role | aut |
| author_sort | Litvinov, Vil'iam G. 1934- |
| author_variant | v g l vg vgl |
| building | Verbundindex |
| bvnumber | BV013152949 |
| classification_rvk | SK 620 SK 920 |
| classification_tum | MTA 309f MAT 671f MAT 355f |
| ctrlnum | (OCoLC)247739650 (DE-599)BVBBV013152949 |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV013152949 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T03:50:22Z |
| institution | BVB |
| isbn | 3764361999 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008961723 |
| oclc_num | 247739650 |
| open_access_boolean | |
| owner | DE-703 DE-706 DE-91G DE-BY-TUM DE-634 DE-83 DE-11 |
| owner_facet | DE-703 DE-706 DE-91G DE-BY-TUM DE-634 DE-83 DE-11 |
| physical | XXII, 522 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Litvinov, Vil'iam G. 1934- Verfasser (DE-588)121954730 aut Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics William G. Litvinov Basel ; Boston ; Berlin Birkhäuser 2000 XXII, 522 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 119 Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Operator theory 119 (DE-604)BV000000970 119 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008961723&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Litvinov, Vil'iam G. 1934- Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics Operator theory Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4128130-5 |
| title | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |
| title_auth | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |
| title_exact_search | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |
| title_full | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics William G. Litvinov |
| title_fullStr | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics William G. Litvinov |
| title_full_unstemmed | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics William G. Litvinov |
| title_short | Optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |
| title_sort | optimization in elliptic problems with applications to mechanics of deformable bodies and fluid mechanics |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Elliptische Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008961723&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT litvinovviliamg optimizationinellipticproblemswithapplicationstomechanicsofdeformablebodiesandfluidmechanics |