Spherical means for PDEs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Utrecht
VSP
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 188 S. |
| ISBN: | 9067642118 |
Staff View
MARC
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| 100 | 1 | |a Sabel'fel'd, Karl K. |d 1953- |e Verfasser |0 (DE-588)121181529 |4 aut | |
| 245 | 1 | 0 | |a Spherical means for PDEs |c K. K. Sabelfeld and I. A. Shalimova |
| 264 | 1 | |a Utrecht |b VSP |c 1997 | |
| 300 | |a VIII, 188 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Shalimova, I. A. |e Sonstige |4 oth | |
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Record in the Search Index
| _version_ | 1804140424844017664 |
|---|---|
| adam_text | Contents
1. Introduction 1
2. Scalar second order PDEs 5
2.1. Spherical mean value relations for the Laplace equation and
integral formulation of the Dirichlet problem 5
2.1.1. Direct spherical mean value relation 6
2.1.2. Converse mean value theorem 13
2.1.3. Integral equation equivalent to the Dirichlet problem 15
2.1.4. Poisson-Jensen formula 17
2.2. The diffusion and Helmholtz equations 19
2.2.1. Diffusion equation 20
2.2.2. Helmholtz equation 21
2.3. Generalized second order elliptic equations 23
2.4. Parabolic equations 26
2.4.1. Heat equation 26
2.4.2. Parabolic equations with variable coefficients ... 32
2.4.3. Expansion of the parabolic means 35
3. High-order elliptic equations 39
3.1. Balayage operator 39
3.2. The biharmonic equation 41
3.2.1. Direct spherical mean value relation 42
3.2.2. The generalized Poisson formula 44
3.2.3. Rigid fixing of the boundary 49
3.2.4. Nonhomogeneous biharmonic equation 52
jv Contents
3.3. Fourth order equation governing the bending of a plate on
an elastic base surface 54
3.4. Metaharmonic equations 59
3.4.1. Polyharmonic equation 59
3.4.2. General case 62
4. Triangular systems of elliptic equations 68
4.1. A one-component diffusion system 68
4.2. A two-component diffusion system 70
4.3. A coupled biharmonic-harmonic equation 73
5. Systems of elasticity theory 75
5.1. The Lame equation 75
5.1.1. Direct spherical mean value theorem 75
5.1.2. Converse spherical mean value theorem 81
5.2. Pseudo-vibration elastic equation 84
5.3. Thermo-elastic equation 92
6. The generalized Poisson formula for the Lame equation 94
6.1. Plane elasticity 94
6.2. Generalized spatial Poisson formula for the Lame equation 105
6.3. An alternative derivation of the Poisson formula 122
7. Spherical means for the stress and strain tensors 127
7.1. Spherical means for the displacement components through
the displacement vector 127
7.2. Mean value relation for the stress and strain tensors through
the displacement vector 131
7.2.1. Mean value relation for the strain components . . 131
7.2.2. Mean value relation for the stress components . . 137
7.3. Mean value relations for the stress components in terms of
the surface tractions 138
Contents V
8. Applications to the Random Walk on Spheres method 150
8.1. Spherical mean as a mathematical expectation 150
8.2. Iterations of the spherical mean operator 151
8.3. The Random Walk on Spheres algorithm 152
8.3.1. The Random Walk on Spheres process for the Dirich-
let problem 152
8.3.2. Inhomogeneous case 164
8.4. Biharmonic equation 166
8.5. Random Walk on Spheres method for the Lame equation 168
8.5.1. Naive generalization 168
8.5.2. A modification of the algorithm 170
8.5.3. Non-isotropic Random Walk on Spheres 173
8.5.4. Branching process 175
8.5.5. Analytical continuation with respect to the spectral
parameter 178
8.6. Alternative Schwarz procedure 181
Bibliography 185
|
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| author_GND | (DE-588)121181529 |
| author_facet | Sabel'fel'd, Karl K. 1953- |
| author_role | aut |
| author_sort | Sabel'fel'd, Karl K. 1953- |
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| building | Verbundindex |
| bvnumber | BV024446241 |
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| id | DE-604.BV024446241 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:59:46Z |
| institution | BVB |
| isbn | 9067642118 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018422956 |
| oclc_num | 636834842 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | VIII, 188 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | VSP |
| record_format | marc |
| spelling | Sabel'fel'd, Karl K. 1953- Verfasser (DE-588)121181529 aut Spherical means for PDEs K. K. Sabelfeld and I. A. Shalimova Utrecht VSP 1997 VIII, 188 S. txt rdacontent n rdamedia nc rdacarrier Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s 1\p DE-604 Shalimova, I. A. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sabel'fel'd, Karl K. 1953- Spherical means for PDEs Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4044779-0 |
| title | Spherical means for PDEs |
| title_auth | Spherical means for PDEs |
| title_exact_search | Spherical means for PDEs |
| title_full | Spherical means for PDEs K. K. Sabelfeld and I. A. Shalimova |
| title_fullStr | Spherical means for PDEs K. K. Sabelfeld and I. A. Shalimova |
| title_full_unstemmed | Spherical means for PDEs K. K. Sabelfeld and I. A. Shalimova |
| title_short | Spherical means for PDEs |
| title_sort | spherical means for pdes |
| topic | Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Randwertproblem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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