Mathematical analysis and numerical methods for science and technology: 6 Evolution problems ; 2
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London
Springer-Verlag
1993
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 485 S. |
| ISBN: | 3540502068 0387502068 |
Staff View
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| 245 | 1 | 0 | |a Mathematical analysis and numerical methods for science and technology |n 6 |p Evolution problems ; 2 |c Robert Dautray ; Jacques-Louis Lions |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London |b Springer-Verlag |c 1993 | |
| 300 | |a XII, 485 S. | ||
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| adam_text | TABLE OF CONTENTS CHAPTER XIX. THE LINEARISED NAVIER-STOKES EQUATIONS
INTRODUCTION 1 §1. THE STATIONARY NAVIER-STOKES EQUATIONS: THE LINEAR
CASE 1 1. FUNCTIONAL SPACES 2 2. EXISTENCE AND UNIQUENESS THEOREM 11 3.
THE PROBLEM OF L A REGULARITY 18 §2. THE EVOLUTIONARY NAVIER-STOKES
EQUATIONS: THE LINEAR CASE 21 1. FUNCTIONAL SPACES AND TRACE THEOREMS 21
2. EXISTENCE AND UNIQUENESS THEOREM 25 3. L 2 -REGULARITY RESULT 28 §3.
ADDITIONAL RESULTS AND REVIEW 31 1. THE VARIATIONAL APPROACH 31 2. THE
FUNCTIONAL APPROACH 31 3. THE PROBLEM OF L A REGULARITY FOR THE
EVOLUTIONARY NAVIER-STOKES EQUATIONS: THE LINEARISED CASE 33 CHAPTER XX.
NUMERICAL METHODS FOR EVOLUTION PROBLEMS §1. GENERAL POINTS 35 1.
DISCRETISATION IN SPACE AND TIME 35 2. CONVERGENCE, CONSISTENCY AND
STABILITY 36 3. EQUIVALENCE THEOREM 37 4. COMMENTS 39 5. SCHEMES WITH
CONSTANT COEFFICIENTS AND STEP SIZE 40 6. THE SYMBOL OF A DIFFERENCE
SCHEME 41 7. THE VON NEUMANN STABILITY CONDITION 42 8. THE KREISS
STABILITY CONDITION 43 9. THE CASE OF MULTILEVEL SCHEMES 44 10.
CHARACTERISATION OF A SCHEME OF ORDER Q 44 §2. PROBLEMS OF FIRST ORDER
IN TIME 45 1. INTRODUCTION 45 DU D 2 U 2. MODEL EQUATION *-^ = 0 FOR XE
U 46 H DT DX 2 3. THE BOUNDARY VALUE PROBLEM FOR EQUATION -* * -Z = 0 54
OT OX 4. EQUATION WITH VARIABLE COEFFICIENTS AND SCHEMES WITH VARIABLE
STEP-SIZE 56 5. THE HEAT FLOW EQUATION IN TWO SPACE DIMENSIONS 59 6.
ALTERNATING DIRECTION AND FRACTIONAL STEP METHODS 62 7. INTERNAL
APPROXIMATION SCHEMES 65 8. INTEGRATION OF SYSTEMS OF STIFF DIFFERENTIAL
EQUATIONS 68 9. COMMENTS 74 §3. PROBLEMS OF SECOND ORDER IN TIME 75 1.
INTRODUCTION 75 D 2 U 1 D 2 U 2. THE MODEL EQUATION *, T * C Z *^ = 0
FOR XE U 76 DT 2 DX 2 3. THE WAVE EQUATION IN TWO SPACE DIMENSIONS 82 4.
INTERNAL APPROXIMATION SCHEMES 84 5. THE NEWMARK SCHEME 86 6. THE WAVE
EQUATION WITH VISCOSITY 90 7. THE WAVE EQUATION COUPLED TO A HEAT FLOW
EQUATION 92 8. COMMENTS 95 §4. THE ADVECTION EQUATION 96 1. INTRODUCTION
96 2. SOME EXPLICIT SCHEMES FOR THE CAUCHY PROBLEM IN ONE SPACE
DIMENSION 97 3. POSITIVE-TYPE SCHEMES AND STABLE SCHEMES IN L([R) 105
4. SOME EXPLICIT SCHEMES 108 5. THE PROBLEM WITH BOUNDARY CONDITIONS 110
6. PHASE AND AMPLITUDE ERROR. SCHEMES OF ORDER GREATER THAN TWO . 113 DU
DU 7. NONLINEAR SCHEMES FOR THE EQUATION * + A * = 0 118 AT OX 8.
DIFFERENCE SCHEMES FOR THE CAUCHY PROBLEM WITH MANY SPACE VARIABLES 121
§5. SYMMETRIC FRIEDRICHS SYSTEMS 125 1. INTRODUCTION 125 2. SUMMARY OF
SYMMETRIC FRIEDRICHS SYSTEMS. 125 3. FINITE DIFFERENCE SCHEMES FOR THE
CAUCHY PROBLEM 128 4. APPROXIMATION OF BOUNDARY CONDITIONS IN THE CASE
WHERE Q = ]0, 1[ 131 5. MAXWELL S EQUATIONS 132 6. REMARKS 136 §6. THE
TRANSPORT EQUATION 137 1. INTRODUCTION 137 2. STATIONARY EQUATION IN
ONE-DIMENSIONAL PLANE GEOMETRY 139 3. THE EVOLUTION EQUATION IN
ONE-DIMENSIONAL PLANE GEOMETRY ... 143 4. THE EQUATION IN
ONE-DIMENSIONAL SPHERICAL GEOMETRY 146 5. ITERATIVE SOLUTION OF SCHEMES
APPROXIMATING THE TRANSPORT EQUATION 150 6. THE TWO-DIMENSIONAL EQUATION
154 7. OTHER METHODS 158 8. COMMENTS 166 §7. NUMERICAL SOLUTION OF THE
STOKES PROBLEM 167 1. SETTING OF PROBLEM 167 2. AN INTEGRAL METHOD 173
3. SOME FINITE DIFFERENCE METHODS 177 4. FINITE ELEMENT METHODS 183 5.
SOME METHODS USING THE STREAM FUNCTION 194 6. THE EVOLUTIONARY STOKES
PROBLEM 200 CHAPTER XXI. TRANSPORT §1. INTRODUCTION. PRESENTATION OF
PHYSICAL PROBLEMS 209 1. EVOLUTION PROBLEMS IN NEUTRON TRANSPORT 209 2.
STATIONARY PROBLEMS 213 3. PRINCIPAL NOTATION 215 §2. EXISTENCE AND
UNIQUENESS OF SOLUTIONS OF THE TRANSPORT EQUATION. . . 215 1.
INTRODUCTION 215 2. STUDY OF THE ADVECTION OPERATOR A = * V. V 218 3.
SOLUTION OF THE CAUCHY TRANSPORT PROBLEM 226 4. SOLUTION OF THE
STATIONARY TRANSPORT PROBLEM IN THE SUBCRITICAL CASE 240 SUMMARY 248
APPENDIX OF §2. BOUNDARY CONDITIONS IN TRANSPORT PROBLEMS. REFLECTION
CONDITIONS 249 §3. SPECTRAL THEORY AND ASYMPTOTIC BEHAVIOUR OF THE
SOLUTIONS OF EVOLUTION PROBLEMS 262 1. INTRODUCTION 262 2. STUDY OF THE
SPECTRUM OF THE OPERATOR B = * V.V* Z 265 3. STUDY OF THE SPECTRUM OF
THE TRANSPORT OPERATOR IN AN OPEN BOUNDED SET X OF U N 272 4. POSITIVITY
PROPERTIES 285 5. THE PARTICULAR CASE WHERE ALL THE EIGENVALUES ARE REAL
296 6. THE SPECTRUM OF THE TRANSPORT OPERATOR IN A BAND. THE LEHNER-WING
THEOREM 301 7. STUDY OF THE SPECTRUM OF THE TRANSPORT OPERATOR IN THE
WHOLE SPACE: X = U N 306 8. THE SPECTRUM OF THE TRANSPORT OPERATOR ON
THE EXTERIOR OF AN OBSTACLE 321 9. SOME REMARKS ON THE SPECTRUM OF T .
. 324 SUMMARY 334 APPENDIX OF §3. THE CONSERVATIVE MILNE PROBLEM 335 §4.
EXPLICIT EXAMPLES 347 1. THE STATIONARY TRANSPORT PROBLEM IN THE WHOLE
SPACE U 347 2. THE EVOLUTIONARY TRANSPORT PROBLEM IN THE WHOLE SPACE 352
3. THE STATIONARY TRANSPORT PROBLEM IN THE HALF-SPACE BY THE METHOD OF
INVARIANT EMBEDDING 355 4. CASE S METHOD OF GENERALISED
EIGENFUNCTIONS . APPLICATION TO THE CRITICAL DIMENSION IN THE CASE OF A
BAND 363 §5. APPROXIMATION OF THE NEUTRON TRANSPORT EQUATION BY THE
DIFFUSION EQUATION 368 1. PHYSICAL INTRODUCTION 368 2. APPROXIMATION IN
THE CASE OF A MONOKINETIC MODEL OF EVOLUTION EQUATIONS AND OF STATIONARY
TRANSPORT EQUATIONS .... 372 3. GENERALISATION OF SECTION 2 383 4.
CALCULATION OF A CORRECTOR FOR THE STATIONARY PROBLEM AND EXTRAPOLATION
LENGTH 388 5. CONVERGENCE OF THE PRINCIPAL EIGENVALUE OF THE TRANSPORT
OPERATOR 394 6. CALCULATION OF A CORRECTOR FOR THE PRINCIPAL EIGENVALUE
OF THE TRANSPORT OPERATOR 398 7. APPLICATION TO A CRITICAL SIZE PROBLEM
403 8. NUMERICAL EXAMPLE IN THE CASE OF A BAND 405 APPENDIX OF §5 408
BIBLIOGRAPHY 417 PERSPECTIVES 425 ORIENTATION FOR THE READER 426 LIST OF
EQUATIONS 429 TABLE OF NOTATIONS 431 CUMULATIVE INDEX OF VOLUMES 1-6 447
CONTENTS OF VOLUMES 1-5 481
|
| adam_txt |
TABLE OF CONTENTS CHAPTER XIX. THE LINEARISED NAVIER-STOKES EQUATIONS
INTRODUCTION 1 §1. THE STATIONARY NAVIER-STOKES EQUATIONS: THE LINEAR
CASE 1 1. FUNCTIONAL SPACES 2 2. EXISTENCE AND UNIQUENESS THEOREM 11 3.
THE PROBLEM OF L A REGULARITY 18 §2. THE EVOLUTIONARY NAVIER-STOKES
EQUATIONS: THE LINEAR CASE 21 1. FUNCTIONAL SPACES AND TRACE THEOREMS 21
2. EXISTENCE AND UNIQUENESS THEOREM 25 3. L 2 -REGULARITY RESULT 28 §3.
ADDITIONAL RESULTS AND REVIEW 31 1. THE VARIATIONAL APPROACH 31 2. THE
FUNCTIONAL APPROACH 31 3. THE PROBLEM OF L A REGULARITY FOR THE
EVOLUTIONARY NAVIER-STOKES EQUATIONS: THE LINEARISED CASE 33 CHAPTER XX.
NUMERICAL METHODS FOR EVOLUTION PROBLEMS §1. GENERAL POINTS 35 1.
DISCRETISATION IN SPACE AND TIME 35 2. CONVERGENCE, CONSISTENCY AND
STABILITY 36 3. EQUIVALENCE THEOREM 37 4. COMMENTS 39 5. SCHEMES WITH
CONSTANT COEFFICIENTS AND STEP SIZE 40 6. THE SYMBOL OF A DIFFERENCE
SCHEME 41 7. THE VON NEUMANN STABILITY CONDITION 42 8. THE KREISS
STABILITY CONDITION 43 9. THE CASE OF MULTILEVEL SCHEMES 44 10.
CHARACTERISATION OF A SCHEME OF ORDER Q 44 §2. PROBLEMS OF FIRST ORDER
IN TIME 45 1. INTRODUCTION 45 DU D 2 U 2. MODEL EQUATION *-^ = 0 FOR XE
U 46 H DT DX 2 3. THE BOUNDARY VALUE PROBLEM FOR EQUATION -* * -Z = 0 54
OT OX 4. EQUATION WITH VARIABLE COEFFICIENTS AND SCHEMES WITH VARIABLE
STEP-SIZE 56 5. THE HEAT FLOW EQUATION IN TWO SPACE DIMENSIONS 59 6.
ALTERNATING DIRECTION AND FRACTIONAL STEP METHODS 62 7. INTERNAL
APPROXIMATION SCHEMES 65 8. INTEGRATION OF SYSTEMS OF STIFF DIFFERENTIAL
EQUATIONS 68 9. COMMENTS 74 §3. PROBLEMS OF SECOND ORDER IN TIME 75 1.
INTRODUCTION 75 D 2 U 1 D 2 U 2. THE MODEL EQUATION *, T * C Z *^ = 0
FOR XE U 76 DT 2 DX 2 3. THE WAVE EQUATION IN TWO SPACE DIMENSIONS 82 4.
INTERNAL APPROXIMATION SCHEMES 84 5. THE NEWMARK SCHEME 86 6. THE WAVE
EQUATION WITH VISCOSITY 90 7. THE WAVE EQUATION COUPLED TO A HEAT FLOW
EQUATION 92 8. COMMENTS 95 §4. THE ADVECTION EQUATION 96 1. INTRODUCTION
96 2. SOME EXPLICIT SCHEMES FOR THE CAUCHY PROBLEM IN ONE SPACE
DIMENSION 97 3. POSITIVE-TYPE SCHEMES AND STABLE SCHEMES IN L([R) 105
4. SOME EXPLICIT SCHEMES 108 5. THE PROBLEM WITH BOUNDARY CONDITIONS 110
6. PHASE AND AMPLITUDE ERROR. SCHEMES OF ORDER GREATER THAN TWO . 113 DU
DU 7. NONLINEAR SCHEMES FOR THE EQUATION * + A * = 0 118 AT OX 8.
DIFFERENCE SCHEMES FOR THE CAUCHY PROBLEM WITH MANY SPACE VARIABLES 121
§5. SYMMETRIC FRIEDRICHS SYSTEMS 125 1. INTRODUCTION 125 2. SUMMARY OF
SYMMETRIC FRIEDRICHS SYSTEMS. 125 3. FINITE DIFFERENCE SCHEMES FOR THE
CAUCHY PROBLEM 128 4. APPROXIMATION OF BOUNDARY CONDITIONS IN THE CASE
WHERE Q = ]0, 1[ 131 5. MAXWELL'S EQUATIONS 132 6. REMARKS 136 §6. THE
TRANSPORT EQUATION 137 1. INTRODUCTION 137 2. STATIONARY EQUATION IN
ONE-DIMENSIONAL PLANE GEOMETRY 139 3. THE EVOLUTION EQUATION IN
ONE-DIMENSIONAL PLANE GEOMETRY . 143 4. THE EQUATION IN
ONE-DIMENSIONAL SPHERICAL GEOMETRY 146 5. ITERATIVE SOLUTION OF SCHEMES
APPROXIMATING THE TRANSPORT EQUATION 150 6. THE TWO-DIMENSIONAL EQUATION
154 7. OTHER METHODS 158 8. COMMENTS 166 §7. NUMERICAL SOLUTION OF THE
STOKES PROBLEM 167 1. SETTING OF PROBLEM 167 2. AN INTEGRAL METHOD 173
3. SOME FINITE DIFFERENCE METHODS 177 4. FINITE ELEMENT METHODS 183 5.
SOME METHODS USING THE STREAM FUNCTION 194 6. THE EVOLUTIONARY STOKES
PROBLEM 200 CHAPTER XXI. TRANSPORT §1. INTRODUCTION. PRESENTATION OF
PHYSICAL PROBLEMS 209 1. EVOLUTION PROBLEMS IN NEUTRON TRANSPORT 209 2.
STATIONARY PROBLEMS 213 3. PRINCIPAL NOTATION 215 §2. EXISTENCE AND
UNIQUENESS OF SOLUTIONS OF THE TRANSPORT EQUATION. . . 215 1.
INTRODUCTION 215 2. STUDY OF THE ADVECTION OPERATOR A = * V. V 218 3.
SOLUTION OF THE CAUCHY TRANSPORT PROBLEM 226 4. SOLUTION OF THE
STATIONARY TRANSPORT PROBLEM IN THE SUBCRITICAL CASE 240 SUMMARY 248
APPENDIX OF §2. BOUNDARY CONDITIONS IN TRANSPORT PROBLEMS. REFLECTION
CONDITIONS 249 §3. SPECTRAL THEORY AND ASYMPTOTIC BEHAVIOUR OF THE
SOLUTIONS OF EVOLUTION PROBLEMS 262 1. INTRODUCTION 262 2. STUDY OF THE
SPECTRUM OF THE OPERATOR B = * V.V* Z 265 3. STUDY OF THE SPECTRUM OF
THE TRANSPORT OPERATOR IN AN OPEN BOUNDED SET X OF U N 272 4. POSITIVITY
PROPERTIES 285 5. THE PARTICULAR CASE WHERE ALL THE EIGENVALUES ARE REAL
296 6. THE SPECTRUM OF THE TRANSPORT OPERATOR IN A BAND. THE LEHNER-WING
THEOREM 301 7. STUDY OF THE SPECTRUM OF THE TRANSPORT OPERATOR IN THE
WHOLE SPACE: X = U N 306 8. THE SPECTRUM OF THE TRANSPORT OPERATOR ON
THE EXTERIOR OF AN "OBSTACLE" 321 9. SOME REMARKS ON THE SPECTRUM OF T .
. 324 SUMMARY 334 APPENDIX OF §3. THE CONSERVATIVE MILNE PROBLEM 335 §4.
EXPLICIT EXAMPLES 347 1. THE STATIONARY TRANSPORT PROBLEM IN THE WHOLE
SPACE U 347 2. THE EVOLUTIONARY TRANSPORT PROBLEM IN THE WHOLE SPACE 352
3. THE STATIONARY TRANSPORT PROBLEM IN THE HALF-SPACE BY THE METHOD OF
"INVARIANT EMBEDDING" 355 4. CASE'S METHOD OF "GENERALISED
EIGENFUNCTIONS". APPLICATION TO THE CRITICAL DIMENSION IN THE CASE OF A
BAND 363 §5. APPROXIMATION OF THE NEUTRON TRANSPORT EQUATION BY THE
DIFFUSION EQUATION 368 1. PHYSICAL INTRODUCTION 368 2. APPROXIMATION IN
THE CASE OF A MONOKINETIC MODEL OF EVOLUTION EQUATIONS AND OF STATIONARY
TRANSPORT EQUATIONS . 372 3. GENERALISATION OF SECTION 2 383 4.
CALCULATION OF A CORRECTOR FOR THE STATIONARY PROBLEM AND EXTRAPOLATION
LENGTH 388 5. CONVERGENCE OF THE PRINCIPAL EIGENVALUE OF THE TRANSPORT
OPERATOR 394 6. CALCULATION OF A CORRECTOR FOR THE PRINCIPAL EIGENVALUE
OF THE TRANSPORT OPERATOR 398 7. APPLICATION TO A CRITICAL SIZE PROBLEM
403 8. NUMERICAL EXAMPLE IN THE CASE OF A BAND 405 APPENDIX OF §5 408
BIBLIOGRAPHY 417 PERSPECTIVES 425 ORIENTATION FOR THE READER 426 LIST OF
EQUATIONS 429 TABLE OF NOTATIONS 431 CUMULATIVE INDEX OF VOLUMES 1-6 447
CONTENTS OF VOLUMES 1-5 481 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:17:32Z |
| indexdate | 2024-07-09T20:51:13Z |
| institution | BVB |
| isbn | 3540502068 0387502068 |
| language | English |
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| physical | XII, 485 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer-Verlag |
| record_format | marc |
| spelling | Dautray, Robert 1928- (DE-588)133309347 aut Analyse mathématique et calcul numérique pour les sciences et les techniques Mathematical analysis and numerical methods for science and technology 6 Evolution problems ; 2 Robert Dautray ; Jacques-Louis Lions Berlin ; Heidelberg ; New York ; Paris ; Barcelona ; Hong Kong ; London Springer-Verlag 1993 XII, 485 S. txt rdacontent n rdamedia nc rdacarrier Lions, Jacques-Louis 1928-2001 (DE-588)124055397 aut (DE-604)BV013031479 6 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015353955&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dautray, Robert 1928- Lions, Jacques-Louis 1928-2001 Mathematical analysis and numerical methods for science and technology |
| title | Mathematical analysis and numerical methods for science and technology |
| title_alt | Analyse mathématique et calcul numérique pour les sciences et les techniques |
| title_auth | Mathematical analysis and numerical methods for science and technology |
| title_exact_search | Mathematical analysis and numerical methods for science and technology |
| title_exact_search_txtP | Mathematical analysis and numerical methods for science and technology |
| title_full | Mathematical analysis and numerical methods for science and technology 6 Evolution problems ; 2 Robert Dautray ; Jacques-Louis Lions |
| title_fullStr | Mathematical analysis and numerical methods for science and technology 6 Evolution problems ; 2 Robert Dautray ; Jacques-Louis Lions |
| title_full_unstemmed | Mathematical analysis and numerical methods for science and technology 6 Evolution problems ; 2 Robert Dautray ; Jacques-Louis Lions |
| title_short | Mathematical analysis and numerical methods for science and technology |
| title_sort | mathematical analysis and numerical methods for science and technology evolution problems 2 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015353955&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013031479 |
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