Complex integral operators in mathematical physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leipzig u.a.
Barth, Ed. Dt. Verl. der Wiss.
1993
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [291] - 317 |
| Physical Description: | 320 S. |
| ISBN: | 3335003446 |
Staff View
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| 100 | 1 | |a Lanckau, Eberhard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex integral operators in mathematical physics |c by Eberhard Lanckau |
| 264 | 1 | |a Leipzig u.a. |b Barth, Ed. Dt. Verl. der Wiss. |c 1993 | |
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Record in the Search Index
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| adam_text | Contents
0. Introduction 11
0.1. Some types of integral transforms 11
0.2. Complex notation of differential equations 13
Part I
Construction of Integral operators
1. The Riemann transform 19
1.1. Definition of the transform 19
1.1.1. Motivation of the method 19
1.1.2. Definition of the Riemann tranform 20
1.1.3. Definition of associated functions 32
1.2. Existence of the Riemann transform 47
1.2.1. Existence of the transform 47
1.2.2. Remarks on the existence theorem 51
1.3. Representation of the Riemann transform — Examples 52
1.3.1. Two dimensional equations 52
1.3.2. Examples: self adjoint equations 53
1.3.3. Examples: non self adjoint equations 93
1.3.4. Example: general differential equation of second order with constant coefficients 105
1.4. Representation of the Riemann transform by integral transforms 109
1.4.1. Cauchy type integrals 109
1.4.2. Examples 113
1.4.3. Duhamel products 120
1.5. Higher order equations 125
1.5.1. Definition and existence of the Riemann transform 125
1.5.2. Examples 127
2. Other transforms 140
2.1. Bergman s integral operator 140
2.1.1. Construction of the transform 140
2.1.2. Examples: Representation of the transform 147
2.2. Relations to differential operators 154
8 Contents
P a r t II
Application of Integral Operators
3. Plane problems 161
3.1. Construction of particular solutions: transonic flow 161
3.2. A correspondence principle 166
3.2.1. Subsonic flow 166
3.2.2. Filtration flow 175
3.3. Boundary value problems 180
3.3.1. First method: reduction to an integral equation 181
3.3.2. Second method: reduction to a boundary value problem for a holomorphic function 187
3.3.3. Third method: superposition of particular solutions 191
4. Axially symmetric problems 193
4.1. The equation 193
4.2. Specialization of transforms to three dimensional problems 194
4.2.1. The transform 194
4.2.2. Representation of the transform T 197
4.2.3. Solution of a Dirichlet problem 212
4.2.4. Conjugate functions 216
4.2.5. The non characteristic Cauchy problem for parabolic equations in one space variable 219
4.2.6. Higher order equations and system of equations 221
4.3. Formally two dimensional problems 223
4.4. Applications 224
4.4.1. Axially symmetric flow of an incompressible fluid 224
4.4.2. Torsion of axially symmetric bodies 231
4.5. Singularities of generalized axially symmetric potentials 233
5. Instationary process in the plane 237
5.1. Pseudoparabolic equations 237
5.1.1. An example: flows of a viscous fluid 237
5.1.2. An initial boundary value problem for a pseudoparabolic equations 240
5.1.3. Specialization: axially symmetric problems 247
5.2. Approximation of parabolic equations by pseudoparabolic ones 250
6. Boundary value problems for three dimensional equations 256
6.1. Construction of particular solutions 256
6.2. Solution of boundary value problems 266
6.2.1. Superposition of particular solutions 267
6.2.2. Reduction to a boundary value problem for harmonic vectors 269
6.2.3. Reduction to an integral equation 271
7. Concluding remarks: non linear equations 276
Contents 9
Appendix A. Notation of special functions 284
Appendix B. List of Riemann transforms — three dimensional cases 286
Appendix C. Transformations of the Tricomi equation 288
Appendix D 289
References 291
Subject Index 319
|
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| id | DE-604.BV005981904 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:38:01Z |
| institution | BVB |
| isbn | 3335003446 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003756427 |
| oclc_num | 29243746 |
| open_access_boolean | |
| owner | DE-384 DE-91 DE-BY-TUM DE-703 DE-634 |
| owner_facet | DE-384 DE-91 DE-BY-TUM DE-703 DE-634 |
| physical | 320 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Barth, Ed. Dt. Verl. der Wiss. |
| record_format | marc |
| spelling | Lanckau, Eberhard Verfasser aut Complex integral operators in mathematical physics by Eberhard Lanckau Leipzig u.a. Barth, Ed. Dt. Verl. der Wiss. 1993 320 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [291] - 317 Differential equations, Partial Functions of complex variables Integral operators Integral transforms Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Integraloperator (DE-588)4131247-8 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 s Integraloperator (DE-588)4131247-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003756427&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lanckau, Eberhard Complex integral operators in mathematical physics Differential equations, Partial Functions of complex variables Integral operators Integral transforms Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4131247-8 |
| title | Complex integral operators in mathematical physics |
| title_auth | Complex integral operators in mathematical physics |
| title_exact_search | Complex integral operators in mathematical physics |
| title_full | Complex integral operators in mathematical physics by Eberhard Lanckau |
| title_fullStr | Complex integral operators in mathematical physics by Eberhard Lanckau |
| title_full_unstemmed | Complex integral operators in mathematical physics by Eberhard Lanckau |
| title_short | Complex integral operators in mathematical physics |
| title_sort | complex integral operators in mathematical physics |
| topic | Differential equations, Partial Functions of complex variables Integral operators Integral transforms Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Integraloperator (DE-588)4131247-8 gnd |
| topic_facet | Differential equations, Partial Functions of complex variables Integral operators Integral transforms Lineare partielle Differentialgleichung Integraloperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003756427&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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