Operator approach to linear problems of hydrodynamics: 1 Self-adjoint problems for an ideal fluid
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2001
|
| Series: | Operator theory
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 384 S. |
| ISBN: | 3764354062 |
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MARC
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| 100 | 1 | |a Kopačevskij, Nikolaj D. |d 1940- |e Verfasser |0 (DE-588)123015987 |4 aut | |
| 240 | 1 | 0 | |a Operatornye metody v linejnoj gidrodinamike |
| 245 | 1 | 0 | |a Operator approach to linear problems of hydrodynamics |n 1 |p Self-adjoint problems for an ideal fluid |c Nikolay D. Kopachevsky ; Selim G. Krein |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XXIV, 384 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 128 | |
| 490 | 0 | |a Operator theory |v ... | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Fluid dynamics |x Mathematical models | |
| 700 | 1 | |a Krejn, Selim G. |e Verfasser |4 aut | |
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| 830 | 0 | |a Operator theory |v 128 |w (DE-604)BV000000970 |9 128 | |
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| _version_ | 1804128653890551808 |
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| adam_text | OPERATOR APPROACH TO LINEAR PROBLEMS OF HYDRODYNAMICS VOLUME 1:
SELF-ADJOINT PROBLEMS FOR AN IDEAL FLUID NIKOLAY D. KOPACHEVSKY SELIM G.
KREIN BIRKHAUSER VERLAG BASEL * BOSTON * BERLIN TABLE OF CONTENTS VOLUME
I PREFACE V TABLE OF CONTENTS VOLUME I VII VOLUME II XV INTRODUCTION 1
PART I: MATHEMATICAL FOUNDATIONS OF LINEAR HYDRODYNAMICS 5 CHAPTER 1:
OPERATORS ON HILBERT SPACES *; 1.1 GENERAL FACTS 7 1.1.1 THE CONCEPT OF
A HILBERT SPACE 7 1.1.2 THE SPACE L 2 (FT) 8 1.1.3 ORTHOGONALITY.
PROJECTION ONTO A SUBSPACE 9 1.1.4 EQUIVALENT NORMS 10 1.1.5 LINEAR
FUNCTIONAL. RIESZ THEOREM 10 1.1.6 EMBEDDINGS OF SPACES. RIESZ THEOREM
FOR EQUIPMENTS . . . 11 1.1.7 ORTHONORMAL SYSTEMS AND BASES 12 1.1.8
BOUNDED LINEAR OPERATORS 12 1.1.9 ADJOINT OPERATORS 14 1.1.10
SELF-ADJOINT OPERATORS 14 1.1.11 SELF-ADJOINT COMPACT OPERATORS 15
1.1.12 COMPACT OPERATORS, S-NUMBERS 16 VIII TABLE OF CONTENTS 1.1.13
RIESZ BASES AND P-BASES 17 1.1.14 DIRECT SUM OF SUBSPACES. INVARIANT
SUBSPACES 18 1.1.15 EIGEN- AND ASSOCIATED (ROOT) ELEMENTS. ROOT
SUBSPACES . . 19 1.1.16 UNBOUNDED LINEAR OPERATORS 20 1.1.17 RESOLVENT
AND SPECTRUM OF A LINEAR OPERATOR 21 1.1.18 CLASSIFICATION OF POINTS IN
THE SPECTRUM OF A LINEAR OPERATOR 22 1.1.19 SPECTRUM OF A SELF-ADJOINT
OPERATOR. WEYL THEOREM . . . . 23 1.1.20 RIESZ PROJECTIONS 24 1.1.21
SYMMETRIC AND SELF-ADJOINT OPERATORS 25 1.1.22 SPECTRAL DECOMPOSITION OF
SELF-ADJOINT OPERATORS. FUNCTIONS OF OPERATORS 26 1.1.23 SPACES WITH
DEGENERATE SCALAR PRODUCTS. SEMINORMS . . . . 28 1.1.24 EQUIVALENT
CORRECTIONS OF SEMINORMS 29 1.2 SOBOLEV SPACES 29 1.2.1 FINITE FUNCTIONS
30 1.2.2 GENERALIZED DERIVATIVES 30 1.2.3 THE DEFINITION OF SOBOLEV
SPACES 31 1.2.4 THE SPACE Z4(FI). REGIONS OF THE FIRST TYPE 31 1.2.5 THE
SUBSPACEIJG 1 ^) 32 1.2.6 EMBEDDING H 1 ^) INTO L 2 (FI). REGIONS OF THE
SECOND TYPE 34 1.2.7 THE TRACE OPERATOR. REGIONS OF THE THIRD TYPE 34
1.3 SPACES WITH INDEFINITE METRICS 35 1.3.1 J-SPACES 35 1.3.2 UNIFORMLY
DEFINITE SUBSPACES 37 1.3.3 J-ORTHONORMAL SYSTEMS AND BASES 37 1.3.4
LINEAR OPERATORS ON J-SPACES 38 1.3.5 INVARIANT SUBSPACES OF
J-SELF-ADJOINT OPERATORS 39 1.3.6 PONTRYAGIN SPACES 39 1.3.7 ON
COMPLETENESS AND BASICITY FOR THE SYSTEM OF ROOT ELEMENTS OF A
./-SELF-ADJOINT OPERATOR 41 1.4 EIGENVALUE PROBLEMS 43 1.4.1 OPERATOR B
IS THE IDENTITY OPERATOR 43 1.4.2 OPERATOR B IS POSITIVE DEFINITE 44
1.4.3 POSITIVITY CONDITION FOR A MATRIX OPERATOR 47 1.4.4 SIMPLIFYING
EQUATIONS WITH AN ALTERNATING OPERATOR . . . . 48 TABLE OF CONTENTS
1.4.5 EQUATIONS IN SPACES WITH INDEFINITE METRICS 49 1.5 EVOLUTION
EQUATIONS IN HILBERT SPACES 51 1.5.1 FIRST ORDER LINEAR DIFFERENTIAL
EQUATIONS WITH BOUNDED OPERATOR COEFFICIENT 51 1.5.2 THE CAUCHY PROBLEM
FOR EQUATIONS WITH UNBOUNDED OPERATORS 52 1.5.3-EQUATIONS WITH A
NEGATIVE SELF-ADJOINT OPERATOR 53 1.5.4 EQUATIONS WITH A DISSIPATIVE
OPERATOR 54 1.5.5 EQUATIONS WITH PERTURBED OPERATORS 55 1.5.6 STABILITY
56 1.5.7 NONHOMOGENEOUS EQUATIONS 57 1.5.8 LINEAR DIFFERENTIAL EQUATIONS
OF THE SECOND ORDER 58 1.5.9 VOLTERRA INTEGRAL EQUATIONS 62 1.6 SPECTRAL
THEORY OF OPERATOR PENCILS 63 1.6.1 EIGEN- AND ASSOCIATED ELEMENTS OF AN
OPERATOR PENCIL . . . 63 1.6.2 ROOT FUNCTIONS 65 1.6.3 FREDHOLM
HOLOMORPHIC OPERATOR-VALUED FUNCTIONS 66 1.6.4 LINEAR PENCILS. THEOREMS
ON COMPLETENESS OF THE SYSTEM OF EIGEN- AND ASSOCIATED ELEMENTS . . . .
. . . . 66 1.6.5 KELDYSH-TYPE N-MULTIPLE COMPLETENESS 68 1.6.6 SPECTRAL
FACTORIZATION OF AN OPERATOR PENCIL 69 1.6.7 COMPLETENESS WITH FINITE
DEFECT OF A SYSTEM OF EIGEN- AND ASSOCIATED ELEMENTS OF AN
OPERATOR-VALUED FUNCTION . * 70 1.6.8 ASYMPTOTIC BEHAVIOR OF BRANCHES OF
EIGENVALUES 71 1.6.9 SELF-ADJOINT OPERATOR PENCILS 72 1.6.10 ON RIESZ
BASICITY OF THE SYSTEM OF EIGENELEMENTS OF A SELF-ADJOINT
OPERATOR-VALUED FUNCTION . 73 1.6.11 VARIATIONAL METHODS FOR
INVESTIGATING CONTINUOUS OPERATOR-VALUED FUNCTIONS 75 1.7 ASYMPTOTIC
METHODS FOR SOLVING EVOLUTION EQUATIONS WITH A SMALL PARAMETER ATTACHED
TO THE DERIVATIVE 76 1.7.1 EQUATIONS WITH A SMALL PARAMETER ATTACHED TO
THE DERIVATIVE 77 1.7.2 SPLITTING OF A HOMOGENEOUS EQUATION 78 1.7.3
SOLVABILITY OF COMMUTATOR EQUATIONS 79 1.7.4 ASYMPTOTIC EXPANSIONS OF
SOLUTIONS 82 TABLE OF CONTENTS 1.7.5 THE SPECIAL CASE OF A SPLITABLE
OPERATOR KERNEL 86 1.7.6 THE CASE OF A NONSTATIONARY PERTURBATION 87
1.7.7 NONHOMOGENEOUS EQUATIONS 87 1.7.8 EIGENVALUE PROBLEMS 90 1.8 A
GENERAL SCHEME FOR SOLVING BOUNDARY VALUE PROBLEMS 93 1.8.1 HILBERT
PAIRS. GENERATING OPERATORS 93 1.8.2 HILBERT PAIRS CONNECTED WITH THE
SPACES H 1 ^) AND L 2 {Q) 95 1.8.3 HILBERT SCALE OF SPACES. SPACE IT 1 /
2 98 1.8.4 SELF-ADJOINT EXTENSIONS OF POSITIVE DEFINITE SYMMETRIC
OPERATORS. GENERALIZED AND WEAK SOLUTIONS OF EQUATIONS . . 99 1.8.5
NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS 101 1.8.6 SPACES OF HARMONIC
FUNCTIONS 103 1.8.7 EMBEDDING AND MAPPING. THE ABSTRACT GREEN FORMULA .
. . 107 CHAPTER 2: FUNDAMENTAL SPACES AND OPERATORS OF LINEAR
HYDRODYNAMICS 2.1 FUNDAMENTAL SPACES AND HYDRODYNAMICS OPERATORS FOR AN
IDEAL FLUID 109 2.1.1 FIELDS WITH FINITE KINETIC ENERGY 110 2.1.2
POTENTIAL FIELDS 110 2.1.3 DIVERGENCE OF FIELDS WITH FINITE KINETIC
ENERGY ILL 2.1.4 THE SPACE OF SOLENOIDAL FIELDS 112 2.1.5 LAPLACE
OPERATOR ON THE SPACE ,H L (Q) 112 2.1.6 NORMAL COMPONENT OF A FIELD OH
THE BOUNDARY 113 2.1.7 GREEN FORMULA FOR THE LAPLACE OPERATORS. HARMONIC
FIELDS 114 2.1.8 WEYL DECOMPOSITION 115 2.1.9 APPROXIMATION BY SMOOTH
FIELDS 116 2.1.10 THE SPACE OF VELOCITY FIELDS FOR AN IDEAL FLUID IN AN
OPEN CONTAINER 117 2.1.11 SYSTEMS OF NONMIXING FLUIDS , 118 2.1.12
SPACES OF VELOCITY FIELDS FOR SYSTEMS OF NONMIXING IDEAL FLUIDS 124 2.2
SPACES AND HYDRODYNAMICS OPERATORS FOR A VISCOUS FLUID . . . . 125 2.2.1
FORCES OF INTERNAL FRICTION. ENERGY DISSIPATION . . . . . . . 126 2.2.2
DIVERGENCE OPERATOR. SOLENOIDAL FIELDS 127 2.2.3 VECTOR LAPLACE
OPERATOR. GREEN FORMULA 128 TABLE OF CONTENTS XI 2.2.4 MOVEMENT OF A
VISCOUS FLUID IN A CLOSED CONTAINER. KORN IDENTITY AND KORN INEQUALITY
. 129 2.2.5 STOKES OPERATOR 131 2.2.6 SPACES OF VELOCITY FIELDS FOR A
VISCOUS INCOMPRESSIBLE FLUID IN AN OPEN CONTAINER 132 2.2.7 MAIN
BOUNDARY VALUE PROBLEMS FOR THE FLUID MOVEMENT IN AN OPEN CONTAINER 134
2.2.8 SPACES OF VELOCITY FIELDS FOR A SYSTEM OF VISCOUS FLUIDS . . . 138
APPENDIX A: REMARKS AND REFERENCE COMMENTS TO PART I A.I CHAPTER 1 143
A.2 CHAPTER 2 146 PART II: MOTION OF BODIES WITH CAVITIES CONTAINING
IDEAL FLUIDS . . 149 CHAPTER 3: OSCILLATIONS OF A HEAVY IDEAL FLUID IN
STATIONARY AND NONSTATIONARY CONTAINERS 3.1 EQUATIONS OF THE MOTION OF A
RIGID BODY WITH A CAVITY FILLED WITH AN INCOMPRESSIBLE FLUID 151 3.1.1
BASIC CONCEPTS OF KINEMATICS 152 3.1.2 EQUATIONS OF MOTION FOR AN
INCOMPRESSIBLE FLUID 153 3.1.3 BOUNDARY CONDITIONS 154 3.1.4 MOTION
EQUATIONS FOR A GYROSTATE 155 3.1.5 DYNAMICS EQUATIONS OF THE SYSTEM
BODY + FLUID I WITH A PARTIALLY FILLED CAVITY 158 3.1.6 TRANSITION TO
UNDIMENSIONAL VARIABLES 163 3.2 MOTION OF AN IDEAL FLUID IN A CLOSED
STATIONARY CONTAINER . . . . 164 3.2.1 BASIC EQUATIONS 164 3.2.2
EXISTENCE OF SOLUTIONS 165 3.3 SMALL MOVEMENTS OF AN IDEAL FLUID IN AN
OPEN IMMOVABLE CONTAINER 166 3.3.1 STATEMENT OF THE PROBLEM AND THE
BASIC EQUATIONS 166 3.3.2 PROJECTION OF EULER EQUATIONS 167 3.3.3
EXISTENCE OF SOLUTIONS 168 3.3.4 PROPER OSCILLATIONS 170 3.4 SMALL JOINT
MOVEMENTS OF A FLUID AND A CONTAINER 171 3.4.1 STATEMENT OF THE PROBLEM
AND THE BASIC EQUATIONS 171 3.4.2 FINDING THE VELOCITY FIELD AND THE
PRESSURE 172 XII TABLE OF CONTENTS 3.4.3 DEFINING THE MOTION LAW OF THE
BODY 173 3.4.4 ZHUKOVSKY POTENTIALS ... ... . 174 3.5 SMALL JOINT
MOVEMENTS AROUND A FIXED POINT OF A BODY AND A FLUID PARTIALLY FILLING
THE CAVITY 174 3.5.1 STATEMENT OF THE PROBLEM AND THE BASIC EQUATIONS
175 3.5.2 THE LAW OF FULL ENERGY BALANCE 176 3.5.3 PROJECTING EULER
EQUATIONS 177 3.5.4 KINETIC MOMENT EQUATION 178 3.5.5 INVESTIGATING THE
COMPLETE SYSTEM OF MOTION EQUATIONS . . 179 3.5.6 PROPER OSCILLATIONS
184 3.5.7 SOLVING THE EVOLUTION PROBLEM 187 3.6 OSCILLATIONS OF A SYSTEM
OF FLUIDS IN AN IMMOVABLE CONTAINER . . . 189 3.6.1 STATEMENT OF THE
PROBLEM 190 3.6.2 ORTHOGONAL PROJECTION METHOD 191 3.6.3 TRANSITION TO
OPERATOR EQUATION 193 3.6.4 PROPER OSCCILATIONS 194 3.6.5 SMALL
MOVEMENTS OF STABLE SYSTEMS 196 CHAPTER 4: PROBLEMS ON OSCILLATIONS OF
CAPILLARY FLUIDS AND PROBLEMS ON HYDROELASTICITY IN IMMOVABLE CONTAINERS
4.1 OSCILLATIONS OF A CAPILLARY FLUID IN A RIGID CONTAINER 199 4.1.1 ON
THE EQUILIBRIUM STATE 200 4.1.2 STATEMENT OF THE PROBLEM ON SMALL
OSCILLATIONS 201 4.1.3 LAW OF ENERGY BALANCE 203 4.1.4 TRANSITION TO
OPERATOR EQUATION 204 4.1.5 PROPERTIES OF THE POTENTIAL ENERGY OPERATOR
205 4.1.6 PROPER OSCILLATIONS 206 4.1.7 INSTABILITY CONDITIONS OF THE
SYSTEM 208 4.1.8 SOLVABILITY OF THE EVOLUTION PROBLEM 208 4.1.9
OSCILLATIONS OF A SYSTEM OF CAPILLARY FLUIDS 209 4.2 OSCILLATIONS OF
FLUIDS IN CONTAINERS WITH ELASTIC ENDS 213 4.2.1 SOLVING THE STATIC
PROBLEM 213 4.2.2 FORMULATION OF THE PROBLEM ON SMALL OSCILLATIONS 216
4.2.3 ENERGY-PRESERVING LAW 217 4.2.4 OPERATOR EQUATION OF THE PROBLEM
219 4.2.5 PROPERTIES OF THE OPERATORS OF THE PROBLEM 220 4.2.6 PROPER
OSCILLATIONS 221 TABJE OF CONTENTS XIII 4.2.7 EVOLUTION PROBLEM 223
4.2.8 OSCILLATIONS OF A FLUID IN A CONTAINER WITH ONE ELASTIC END 224
4.2.9 OSCILLATIONS OF A SYSTEM OF FLUIDS IN A CONTAINER WITH ELASTIC
PLANE PARTITIONS 226 4.3 OSCILLATIONS OF A FLUID IN A PARTIALLY FILLED
CONTAINER WITH AN ELASTIC BOTTOM 232 4.3.1 DETERMINING THE EQUILIBRIUM
STATE 232 4.3.2 FORMULATION OF THE PROBLEM ON SMALL OSCILLATIONS 234
4.3.3 ON SOLVABILITY OF THE EVOLUTION AND SPECTRAL PROBLEMS . . . 234
4.3.4 OSCILLATIONS OF A CAPILLARY FLUID IN A PARTIALLY FILLED ELASTIC
CONTAINER 237 4.3.5 SYSTEMS OF HEAVY FLUIDS IN A CONTAINER WITH ELASTIC
PLATES 241 4.3.6 SYSTEMS OF CAPILLARY FLUIDS IN A CONTAINER WITH ELASTIC
ENDS 244 4.3.7 COMPOUND SYSTEMS OF PLATE-PARTITIONS AND NONMIXING FLUIDS
246 CHAPTER 5: OTHER OPERATOR APPROACHES TO HYDRODYNAMICS PROBLEMS OF
IDEAL FLUIDS 5.1 PLANE PROBLEMS ON PROPER OSCILLATIONS OF A HEAVY FLUID
IN A CHANNEL. AN APPLICATION OF THE STREAM FUNCTION 249 5.1.1. SPECTRAL
PROBLEM FOR THE STREAM FUNCTION 249 5.1.2. PROPERTIES OF NODAL LINES OF
STREAM EIGENFUNCTIONS . . . . 252 5.1.3. ESTIMATES OF EIGENVALUES 256
5.2 SHALLOW WATER THEORY IN PROBLEMS ON OSCILLATIONS OF HEAVY IDEAL
FLUIDS IN BOUNDED REGIONS 257 5.2.1. FORMULATION OF THE PROBLEM WITH A
SMALL PARAMETER . . . . 257 5.2.2. ASYMPTOTIC SOLUTION IN FIRST
APPROXIMATION 259 5.2.3. FORMULAS FOR CALCULATING SECOND ORDER
APPROXIMATIONS . . 261 5.2.4. PLANE PROBLEMS 263 5.2.5. EXAMPLES 264
5.2.6. SYSTEMS OF NONMIXING FLUIDS 265 5.3 OSCILLATIONS OF A SYSTEM
FLUID-GAS IN A BOUNDED REGION . . . . 270 5.3.1. FORMULATION OF THE
INITIAL BOUNDARY VALUE PROBLEM . . . . 270 5.3.2. FORMULATION OF THE
SPECTRAL PROBLEM 272 XIV TABIE OF CONTENTS 5.3.3. TRANSITION TO A SYSTEM
OF OPERATOR EQUATIONS 274 5.3.4 THEOREM ON SPECTRUM 276 5.3.5
VARIATIONAL PRINCIPLES FOR EIGENVALUES 278 CHAPTER 6: OSCILLATIONS OF AN
IDEAL ROTATING FLUID 6.1 MOTION OF FLUIDS IN ROTATING CONTAINERS 281
6.1.1 STATEMENT OF THE PROBLEM AND THE MAIN EQUATIONS 281 6.1.2.
EXISTENCE OF SOLUTIONS 282 6.1.3 NORMAL OSCILLATIONS 284 6.2 MOTION OF A
GYROSTATE SIMILAR TO UNIFORM ROTATION ABOUT A FIXED AXIS 287 6.2.1
STATEMENT OF THE PROBLEM 287 6.2.2 TRANSITION TO THE EVOLUTION EQUATION
IN A HILBERT SPACE . . . 288 6.2.3 PROPERTIES OF THE OPERATORS IN THE
PROBLEM 289 6.2.4 EXISTENCE OF SOLUTION TO THE BOUNDARY VALUE PROBLEM .
. . . 289 6.3 ROTATION OF A FLUID IN A PARTIALLY FILLED CONTAINER 290
6.3.1 ON THE EQUILIBRIUM STATE 290 6.3.2 STATEMENT OF THE PROBLEM ON
SMALL OSCILLATIONS 292 6.3.3 METHOD OF ORTHOGONAL PROJECTION . 294 6.3.4
PROPERTIES OF THE OPERATORS OF THE PROBLEM 297 6.3.5 SYSTEMS OF
NONMIXING FLUIDS 299 6.3.6 TRANSITION TO AN OPERATOR EQUATION AND
PROPERTIES OF THE OPERATORS OF THE PROBLEM 302 6.4 SOLVING THE INITIAL
BOUNDARY VALUE PROBLEM 310 6.4.1 GENERALIZED SOLUTION OF THE OPERATOR
EQUATION 310 6.4.2 SMALL MOVEMENTS OF FLUID IN A PARTIALLY FILLED
CONTAINER . . 313 6.4.3 ON THE STRUCTURE OF THE SPECTRUM OF A VORTICAL
OPERATOR . . 313 6.4.4 CLASSES OF FREE MOVEMENTS 316 6.4.5 FREE
MOVEMENTS OF A SYSTEM OF FLUIDS 318 6.5 SELF-ADJOINT OPERATOR PENCILS
GENERATED BY PROBLEMS ON OSCILLATIONS OF A ROTATING IDEAL FLUID 321
6.5.1 THE MAIN OPERATOR PENCIL 321 6.5.2 ON THE SPECTRUM OF THE OPERATOR
PENCIL 322 6.5.3 OPERATOR PENCILS WITH ANALYTIC PERTURBATIONS 323 6.5.4
FACTORIZATION OF THE OPERATOR PENCIL . . 325 6.5.5 SYSTEMS OF
EIGENELEMENTS WITH DEFECT BASICITY 327 TABLE OF CONTENTS XV 6.5.6
DOUBLE-SIDED ESTIMATES OF POSITIVE AND NEGATIVE EIGENVALUES . 328 6.5.7
ON THE ESSENTIAL SPECTRUM OF THE PROBLEM 331 6.6 PROPER OSCILLATIONS OF
A ROTATING FLUID 333 6.6.1 SURFACE AND INTERNAL WAVES 333 6.6.2
PROPERTIES OF THE SURFACE WAVES 335 6.6.3 ON EXISTENCE AND PROPERTIES OF
INTERNAL WAVES 338 6.6.4 OSCILLATIONS OF A SYSTEM OF NONMIXING FLUIDS
341 APPENDIX B: REMARKS AND REFERENCE COMMENTS TO PART II B.I CHAPTER 3
345 B.2 CHAPTER 4 347 B.3 CHAPTER 5 350 B.4 CHAPTER 6 350 STANDARD
REFERENCE TEXTS 355 BIBLIOGRAPHY 357 LIST OF SYMBOLS . . . . 375 SUBJECT
INDEX 379
|
| any_adam_object | 1 |
| author | Kopačevskij, Nikolaj D. 1940- Krejn, Selim G. |
| author_GND | (DE-588)123015987 |
| author_facet | Kopačevskij, Nikolaj D. 1940- Krejn, Selim G. |
| author_role | aut aut |
| author_sort | Kopačevskij, Nikolaj D. 1940- |
| author_variant | n d k nd ndk s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV013824346 |
| callnumber-first | T - Technology |
| callnumber-label | TA357 |
| callnumber-raw | TA357.K563413 2001 |
| callnumber-search | TA357.K563413 2001 |
| callnumber-sort | TA 3357 K563413 42001 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)314034989 (DE-599)BVBBV013824346 |
| dewey-full | 532/.5/01515724 532.501515724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.5/01515724 532.501515724 |
| dewey-search | 532/.5/01515724 532.501515724 |
| dewey-sort | 3532 15 71515724 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV013824346 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:52:40Z |
| institution | BVB |
| isbn | 3764354062 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009454398 |
| oclc_num | 314034989 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-83 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-83 DE-11 |
| physical | XXIV, 384 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Kopačevskij, Nikolaj D. 1940- Verfasser (DE-588)123015987 aut Operatornye metody v linejnoj gidrodinamike Operator approach to linear problems of hydrodynamics 1 Self-adjoint problems for an ideal fluid Nikolay D. Kopachevsky ; Selim G. Krein Basel [u.a.] Birkhäuser 2001 XXIV, 384 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 128 Operator theory ... Mathematisches Modell Fluid dynamics Mathematical models Krejn, Selim G. Verfasser aut (DE-604)BV013824345 1 Operator theory 128 (DE-604)BV000000970 128 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kopačevskij, Nikolaj D. 1940- Krejn, Selim G. Operator approach to linear problems of hydrodynamics Operator theory Mathematisches Modell Fluid dynamics Mathematical models |
| title | Operator approach to linear problems of hydrodynamics |
| title_alt | Operatornye metody v linejnoj gidrodinamike |
| title_auth | Operator approach to linear problems of hydrodynamics |
| title_exact_search | Operator approach to linear problems of hydrodynamics |
| title_full | Operator approach to linear problems of hydrodynamics 1 Self-adjoint problems for an ideal fluid Nikolay D. Kopachevsky ; Selim G. Krein |
| title_fullStr | Operator approach to linear problems of hydrodynamics 1 Self-adjoint problems for an ideal fluid Nikolay D. Kopachevsky ; Selim G. Krein |
| title_full_unstemmed | Operator approach to linear problems of hydrodynamics 1 Self-adjoint problems for an ideal fluid Nikolay D. Kopachevsky ; Selim G. Krein |
| title_short | Operator approach to linear problems of hydrodynamics |
| title_sort | operator approach to linear problems of hydrodynamics self adjoint problems for an ideal fluid |
| topic | Mathematisches Modell Fluid dynamics Mathematical models |
| topic_facet | Mathematisches Modell Fluid dynamics Mathematical models |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013824345 (DE-604)BV000000970 |
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