Hypersingular integral equations and their applications:
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2004
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 396 S. graph. Darst. |
| ISBN: | 0415309980 |
Internformat
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| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2004 | |
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Datensatz im Suchindex
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| adam_text | HYPERSINGULAR INTEGRAL EQUATIONS AND THEIR APPLICATIONS I.K. LIFANOV
L.N. POLTAVSKII G.M. VAINIKKO CHAPMAN & HALL/CRC A CRC PRESS COMPANY
BOCA RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS PREFACE VIII
AUTHORS IX CHAPTER 1. SINGULAR INTEGRALS AND INTEGRAL EQUATIONS 1 1.1.
SOME FACTS FROM THE THEORY OF ONE-DIMENSIONAL INTEGRALS 1 1.2.
ONE-DIMENSIONAL EQUATIONS 5 1.3. SOME FACTS FROM THE THEORY OF
MULTI-DIMENSIONAL INTEGRALS 9 1.4. TWO-DIMENSIONAL EQUATIONS 16 CHAPTER
2. SOBOLEV-SLOBODETSKII SPACES 27 2.1. GENERALIZED FUNCTIONS 27 2.2.
FOURIER TRANSFORMATION 34 2.3. SOBOLEV-SLOBODETSKII SPACES 42 2.4.
SOBOLEV-SLOBODETSKII SPACES ON MANIFOLDS 53 CHAPTER 3. HYPERSINGULAR
INTEGRAL EQUATIONS 55 3.1. PSEUDODIFFERENTIAL OPERATORS AND THEIR
PROPERTIES 55 3.2. CHANGING VARIABLES IN PSEUDODIFFERENTIAL OPERATORS 67
3.3. PSEUDODIFFERENTIAL AND HYPERSINGULAR INTEGRAL EQUATIONS 77 CHAPTER
4. NEUMANN PROBLEM AND INTEGRAL EQUATIONS WITH DOUBLE LAYER POTENTIAL 95
INTRODUCTION 95 4.1. REDUCTION OF THE NEUMANN PROBLEM TO A HYPERSINGULAR
EQUATION 95 4.2. THE NOETHERIAN PROPERTY OF THE PRANDTL OPERATOR 105
4.3. INDEX OF THE PRANDTL OPERATOR 111 4.4. EQUATION OF THE DOUBLE LAYER
POTENTIAL IN THE PLANE CASE 116 CHAPTER 5. SPACES OF FRACTIONAL
QUOTIENTS AND THEIR PROPERTIES 121 5.1. DISCRETE FOURIER TRANSFORMATION
AND PSEUDO-DIFFERENCE OPERATORS 121 5.2. SPECIAL TRIGONOMETRIC SERIES
126 5.3. SPACES OF FRACTIONAL QUOTIENTS M(R, H) 131 5.4. INTEGRAL
PROJECTOR 139 5.5. SPACES TIL (R, H, Q. H ) AND M(R, H, Q. H ) 149 5.6.
WEIGHTED SPACES , 164 CHAPTER 6. DISCRETE OPERATORS IN QUOTIENT SPACES
169 6.1. BOUNDED OPERATOR FAMILIES IN QUOTIENT SPACES M(R, H) 169 6.1.1.
ONE-DIMENSIONAL DISCRETE SINGULAR OPERATORS 169 6.1.2. MULTIDIMENSIONAL
DISCRETE SINGULAR OPERATORS 171 6.1.3. DISCRETE VORTEX OPERATORS 176
6.1.4. DIFFERENCE OPERATORS 177 6.2. APPROXIMATION OF OPERATORS 178 VI
CONTENTS 6.3. QUADRATURE FORMULAS IN SOBOLEV-SLOBODETSKII SPACES 184
6.3.1. QUADRATURE FORMULAS FOR INTEGRALS 184 6.3.2. QUADRATURE FORMULAS
FOR SINGULAR INTEGRALS 188 6.3.3. QUADRATURE FORMULAS FOR HYPERSINGULAR
INTEGRALS 189 CHAPTER 7. STABILITY OF DISCRETE OPERATORS IN QUOTIENT
SPACES 193 7.1. CONVERGENCE OF APPROXIMATE SOLUTIONS AND THE EXISTENCE
OF SOLUTIONS OF OPERATOR EQUATIONS 193 7.2. STABILITY OF DISCRETE
OPERATORS IN QUOTIENT SPACES 198 7.2.1. DISCRETE VORTEX OPERATORS 198
7.2.2. ITERATED DIFFERENCE LAPLACE OPERATOR OF ORDER M 200 7.2.3
HYPERSINGULAR OPERATORS 202 7.2.4. SECOND ORDER ELLIPTIC DIFFERENCE
OPERATOR WITH VARIABLE COEFFICIENTS 202 7.3. SOME EQUATIONS 203 7.3.1.
THE DIRICHLET PROBLEM FOR THE GENERAL SECOND ORDER ELLIPTIC EQUATION 205
7.3.2. CHARACTERISTIC HYPERSINGULAR EQUATION 207 7.3.3. ITERATED LAPLACE
OPERATOR OF ORDER M (THE DIRICHLET PROBLEM) 207 7.3.4. AN EQUATION
RELATED TO DIFFRACTION PROBLEMS 208 CHAPTER 8. ASYMPTOTIC ESTIMATES OF
THE DISCRETE GREEN FUNCTION 211 8.1. RESTRICTION PROBLEMS FOR
PSEUDODIFFERENCE OPERATORS 211 8.2. ESTIMATES OF THE DISCRETE GREEN
FUNCTION FOR THE DISCRETE PRANDTL OPERATOR IN THE HALFPLANE 215 8.3.
ESTIMATES OF THE DISCRETE GREEN FUNCTION FOR THE PRANDTL OPERATORS IN
BOUNDED DOMAINS 222 8.4. ASYMPTOTIC ESTIMATES OF THE DISCRETE GREEN
FUNCTION IN RECTANGULAR DOMAINS 229 8.5. ASYMPTOTIC ESTIMATES OF SPECIAL
MATRICES 235 CHAPTER 9. QUADRATURE FORMULAS FOR SINGULAR AND
HYPERSINGULAR INTEGRALS 247 9.1. INTEGRALS OVER A CLOSED SMOOTH CURVE;
HILBERT INTEGRALS 247 9.2. INTEGRALS OVER AN OPEN-ENDED SMOOTH CURVE 251
9.3. INTEGRALS ARISING IN BOUNDARY VALUE PROBLEMS FOR THE LAPLACE AND
THE HELMHOLTZ EQUATIONS 257 9.4. INTEGRALS ON SMOOTH SURFACES WITH
BORDER 260 CHAPTER 10. NUMERICAL ANALYSIS OF HYPERSINGULAR INTEGRAL
EQUATIONS 271 10.1. CONVERGENCE IN QUOTIENT SPACES FOR EQUATIONS ON A
SMOOTH SURFACE WITH BORDER 271 10.2. NEUMANN PROBLEM FOR THE HELMHOLTZ
EQUATION: CONVERGENCE IN QUOTIENT SPACES FOR THE CORRESPONDING
HYPERSINGULAR INTEGRAL EQUATION 283 10.3. WEAK CONVERGENCE FOR EQUATIONS
IN A PLANE DOMAIN 287 10.4. CONVERGENCE FOR THE MULTHOPFF EQUATION 291
10.5. CONVERGENCE OF THE NUMERICAL SOLUTION IN THE C-NORM 298 10.6.
CONVERGENCE OF DIFFERENCE RATIOS FOR THE NUMERICAL SOLUTION 301 CHAPTER
11. PROBLEMS IN AERODYNAMICS 309 11.1. MATHEMATICAL MODELLING OF FLOW
PAST AN AIRFOIL WITH SUCTION AND PSEUDODIFFERENTIAL OPERATORS 309 11.2.
ELEMENTS OF THE POTENTIAL THEORY IN THE PLANE CASE 317 11.3.
MATHEMATICAL MODELLING OF FLOW PAST AN AIRFOIL WITH SUCTION AND JET
DISCHARGE 334 CONTENTS VII 11.4. NUMERICAL ANALYSIS OF 3D FLOWS PAST
BODIES OF ARBITRARY SHAPE 341 11.5. ELEMENTS OF THE POTENTIAL THEORY IN
THE THREE-DIMENSIONAL CASE 348 11.6. MATHEMATICAL MODELLING AND
NUMERICAL ANALYSIS OF NONSTATIONARY FLOW PAST A SHIP DECK 361 CHAPTER
12. SOME PROBLEMS OF PHYSICS 367 12.1. MATHEMATICAL MODELLING OF
WIDE-BAND ANTENNAS 367 12.2. ANTENNA-DIFFRACTION PROBLEMS AND CURRENT
SOURCES ON THE ANTENNA SURFACE 372 12.3. NUMERICAL SOLUTION OF THE 3D
NEUMANN PROBLEM FOR THE SCALAR HELMHOLTZ EQUATION FOR BODIES OF COMPLEX
SHAPE 376 12.4. CONTACT PROBLEM: IMPRESSION OF A UNIFORMLY MOVING PUNCH
INTO AN ELASTIC HALFPLANE WITH HEAT GENERATION 381 CONCLUSION 389
REFERENCES 391 INDEX 395
|
| any_adam_object | 1 |
| author | Lifanov, Ivan K. Poltavskii, Lev N. Vainikko, Gennadi 1938- |
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| author_facet | Lifanov, Ivan K. Poltavskii, Lev N. Vainikko, Gennadi 1938- |
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| author_sort | Lifanov, Ivan K. |
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| building | Verbundindex |
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| dewey-full | 518.66 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.66 |
| dewey-search | 518.66 |
| dewey-sort | 3518.66 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T22:30:52Z |
| institution | BVB |
| isbn | 0415309980 |
| language | English |
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| physical | VII, 396 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Chapman & Hall/CRC |
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| spelling | Lifanov, Ivan K. Verfasser aut Hypersingular integral equations and their applications I. K. Lifanov; L. N. Poltavskii; G. M. Vainikko Boca Raton [u.a.] Chapman & Hall/CRC 2004 VII, 396 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Integralgleichung (DE-588)4027229-1 gnd rswk-swf Integralgleichung (DE-588)4027229-1 s DE-604 Poltavskii, Lev N. Verfasser aut Vainikko, Gennadi 1938- Verfasser (DE-588)103337075 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019940980&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lifanov, Ivan K. Poltavskii, Lev N. Vainikko, Gennadi 1938- Hypersingular integral equations and their applications Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4027229-1 |
| title | Hypersingular integral equations and their applications |
| title_auth | Hypersingular integral equations and their applications |
| title_exact_search | Hypersingular integral equations and their applications |
| title_full | Hypersingular integral equations and their applications I. K. Lifanov; L. N. Poltavskii; G. M. Vainikko |
| title_fullStr | Hypersingular integral equations and their applications I. K. Lifanov; L. N. Poltavskii; G. M. Vainikko |
| title_full_unstemmed | Hypersingular integral equations and their applications I. K. Lifanov; L. N. Poltavskii; G. M. Vainikko |
| title_short | Hypersingular integral equations and their applications |
| title_sort | hypersingular integral equations and their applications |
| topic | Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019940980&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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