Fundamental solutions for differential operators and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 414 S. graph. Darst. |
| ISBN: | 0817638695 3764338695 |
Internformat
MARC
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| 100 | 1 | |a Kythe, Prem K. |d 1930- |e Verfasser |0 (DE-588)12072362X |4 aut | |
| 245 | 1 | 0 | |a Fundamental solutions for differential operators and applications |c Prem K. Kythe |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a XIX, 414 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Distributions, théorie des (analyse fonctionnelle) |2 ram | |
| 650 | 7 | |a Opérateurs différentiels |2 ram | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential operators | |
| 650 | 4 | |a Theory of distributions (Functional analysis) | |
| 650 | 0 | 7 | |a Differentialoperator |0 (DE-588)4012251-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grundlösung |0 (DE-588)4158392-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialoperator |0 (DE-588)4012251-7 |D s |
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Datensatz im Suchindex
| _version_ | 1804125470956978176 |
|---|---|
| adam_text | Contents
Preface, ix
Notation, xv
Introduction, 1
1. Historical Background, 1
2. Modern Developments, 9
Chapter 1: Some Basic Concepts, 11
1.1. Definitions, 11
1.2. Green s Identities, 13
1.3. Distributions, 15
1.4. Fundamental Solutions, 29
Chapter 2: Linear Elliptic Operators, 37
2.1. Constant Coefficients, 37
2.2. Laplace Operator, 41
2.3. Helmholtz Operator, 44
2.4. Cauchy Riemann Operator, 48
2.5. Nonhomogeneous Operator, 49
2.6. Maximum Principle, 51
2.7. Method of Images, 56
vi CONTENTS
Chapter 3: Linear Parabolic Operators, 60
3.1. Diffusion Operator, 60
3.2. Heat Potentials, 65
3.3. Cauchy Problem, 68
3.4. Maximum Principle, 75
3.5. Schrodinger Operator, 79
3.6. Method of Images, 81
Chapter 4: Linear Hyperbolic Operators, 85
4.1. Wave Operator, 85
4.2. Harmonic Oscillators, 90
4.3. Wave Potentials, 95
4.4. Cauchy Problem, 100
4.5. Wave Propagation, 105
4.6. Maxwell s Equations, 112
Chapter 5: Nonlinear Operators, 117
5.1. Einstein Kolmogorov Operator, 117
5.2. Fokker Plank Operator, 119
5.3. Klein Gordon Operator, 120
5.4. Dirac s Operator, 122
5.5. Transport Equation, 123
5.6. Transport Operator, 128
5.7. Biharmonic Operator, 129
5.8. Nonlinear Wave Equations, 133
5.9. The A function, 135
5.10. Quasihyperbolic Operator, 136
Chapter 6: Elastostatics, 138
6.1. Basic Relations, 138
6.2. Cauchy Navier Operator, 142
6.3. Half Space Solutions, 146
6.4. Axisymmetric Solutions, 150
6.5. Somigliana s Identity, 155
Chapter 7: Elastodynamics, 162
7.1. Elastodynamic Operator, 162
7.2. Wave Structures, 165
7.3. Bernoulli Euler Operator, 170
7.4. Elastoplasticity, 174
7.5. Anisotropic Medium, 177
CONTENTS vii
Chapter 8: Fluid Dynamics, 180
8.1. Navier Stokes Equations, 180
8.2. Aerodynamic Flows, 187
8.3. Non Newtonian Flows, 191
8.4. Porous Media, 196
8.5. Underwater Acoustic Scattering, 202
Chapter 9: Piezoelectrics, 207
9.1. Green s Functions, 208
9.2. Dynamic Piezoelectric Operator, 211
9.3. Fundamental Solutions, 216
9.4. Steady State Solutions, 220
9.5. Piezocrystal Waves, 225
Chapter 10: Boundary Element Methods, 231
10.1. Boundary Integral Equations, 232
10.2. Boundary Element Method, 234
10.3. Poisson Equation, 236
10.4. Transient Fourier Equation, 241
10.5. Laplace Transform BEM, 249
10.6. Elastostatic BEM, 254
10.7. Fracture Mechanics, 259
Chapter 11: Domain Integrals, 266
11.1. Dual Reciprocity Method, 267
11.2. Multiple Reciprocity Method, 274
11.3. Transient DRM, 277
11.4. Transient MRM, 279
11.5. Fourier Series Method, 280
11.6. Complex Variable BEM, 287
Chapter 12: Finite Deflection of Plates, 292
12.1. von Karman Equations, 292
12.2. Boundary Integral Equations, 295
12.3. Large Deflections, 298
12.4. Singularities in Biharmonic Problems, 306
Chapter 13: Miscellaneous Topics, 307
13.1. Poroelasticity, 307
13.2. Heat Conduction, 312
13.3. Thermoelasticity, 320
13.4. Neutron Diffusion, 327
13.5. Biomechanics, 331
viii CONTENTS
Chapter 14: Quasilinear Elliptic Operators, 338
14.1. p Laplacian, 339
14.2. Lane Emden Equation, 344
14.3. Emden Fowler Equation, 349
14.4. Black Hole Solutions, 353
14.5. Einstein Yang Mills Equation, 358
Appendix A: Transforms of Distributions, 364
A.I. Fourier Transform, 364
A.2. Laplace Transform, 372
A.3. Inverse Laplace Transform, 374
Appendix B: Computational Aspects, 376
Appendix C: List of Differential Operators, 387
Bibliography, 391
Index, 409
|
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| discipline | Mathematik |
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| id | DE-604.BV010982642 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:05Z |
| institution | BVB |
| isbn | 0817638695 3764338695 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007349552 |
| oclc_num | 34776067 |
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| owner_facet | DE-91G DE-BY-TUM DE-703 DE-20 DE-824 DE-706 DE-634 DE-11 DE-188 |
| physical | XIX, 414 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kythe, Prem K. 1930- Verfasser (DE-588)12072362X aut Fundamental solutions for differential operators and applications Prem K. Kythe Boston [u.a.] Birkhäuser 1996 XIX, 414 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Distributions, théorie des (analyse fonctionnelle) ram Opérateurs différentiels ram Problèmes aux limites ram Boundary value problems Differential operators Theory of distributions (Functional analysis) Differentialoperator (DE-588)4012251-7 gnd rswk-swf Grundlösung (DE-588)4158392-9 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s Grundlösung (DE-588)4158392-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kythe, Prem K. 1930- Fundamental solutions for differential operators and applications Distributions, théorie des (analyse fonctionnelle) ram Opérateurs différentiels ram Problèmes aux limites ram Boundary value problems Differential operators Theory of distributions (Functional analysis) Differentialoperator (DE-588)4012251-7 gnd Grundlösung (DE-588)4158392-9 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4158392-9 |
| title | Fundamental solutions for differential operators and applications |
| title_auth | Fundamental solutions for differential operators and applications |
| title_exact_search | Fundamental solutions for differential operators and applications |
| title_full | Fundamental solutions for differential operators and applications Prem K. Kythe |
| title_fullStr | Fundamental solutions for differential operators and applications Prem K. Kythe |
| title_full_unstemmed | Fundamental solutions for differential operators and applications Prem K. Kythe |
| title_short | Fundamental solutions for differential operators and applications |
| title_sort | fundamental solutions for differential operators and applications |
| topic | Distributions, théorie des (analyse fonctionnelle) ram Opérateurs différentiels ram Problèmes aux limites ram Boundary value problems Differential operators Theory of distributions (Functional analysis) Differentialoperator (DE-588)4012251-7 gnd Grundlösung (DE-588)4158392-9 gnd |
| topic_facet | Distributions, théorie des (analyse fonctionnelle) Opérateurs différentiels Problèmes aux limites Boundary value problems Differential operators Theory of distributions (Functional analysis) Differentialoperator Grundlösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007349552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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