Diffusion equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1992
|
| Schriftenreihe: | Translations of mathematical monographs
114 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | X, 225 S. |
| ISBN: | 0821845705 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804121383905525760 |
|---|---|
| adam_text | Contents
Preface to the English Edition vii
Preface to the Japanese Edition ix
Introduction 1
§0. Physical background for diffusion equations 1
§ 1. Preparation for the mathematical investigation of diffusion
equations; outline of the contents of this book 10
§2. Preliminary notions and notation 18
§3. Diffusion equations and the definition of fundamental solutions 22
Chapter 1. Fundamental Solutions of Diffusion Equations in
Euclidean Spaces 25
§4. Preliminaries for fundamental solutions 25
§5. Construction of the fundamental solution (in the case of
Euclidean space) 31
Chapter 2. Diffusion Equations in a Bounded Domain 41
§6. Preparatory investigation of boundary conditions 41
§7. Construction of the fundamental solution (in the case of a
bounded domain) 50
§8. Uniqueness of the fundamental solution and the nonnegativity
of the fundamental solution 60
§9. Existence and uniqueness of the solution of inhomogeneous
initial boundary value problems 68
§10. Positivity of the fundamental solution and the strong
maximum principle for diffusion equations 76
§11. Dependence of solutions on the coefficients in the equation, on
the boundary condition, and on the domain where the equation
is considered 85
Chapter 3. Diffusion Equations in Unbounded Domains 91
§12. Construction of a fundamental solution 91
§13. Properties of the fundamental solution, existence of solutions
of inhomogeneous initial boundary value problems 100
V
vi CONTENTS
§14. Fundamental solution in the temporally homogeneous case 111
§15. Eigenfunction expansion associated with the elliptic operator
(A, Bo) in a bounded domain 119
§ 16. Remarks on the case of a domain with piecewise smooth
boundary; examples of eigenfunction expansion 128
§17. Some counterexamples concerning the uniqueness of solutions
and related problems 140
Chapter 4. Elliptic Boundary Value Problems 147
§18. Green s function for elliptic boundary value problems 147
§19. Existence of solutions of elliptic boundary value problems. I 158
§20. Invariant measure for the fundamental solution 166
§21. Existence of solutions of elliptic boundary value problems. II.
The Neumann function 173
§22. Properties of ^ harmonic functions 182
§23. Weak solutions and genuine solutions 195
Chapter 5. Some Related Topics in Vector Analysis 209
§24. Solenoidal and potential components of a vector field 209
§25. Helmholtz decomposition, incompressible flow given boundary
data 214
Supplementary Notes and References 221
Subject Index 225
|
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:57:07Z |
| institution | BVB |
| isbn | 0821845705 |
| language | English |
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| physical | X, 225 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Math. Soc. |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Itô, Seizô Verfasser aut Kakusan-hōteishiki Diffusion equations Seizô Itô Providence, RI American Math. Soc. 1992 X, 225 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 114 Aus dem Japan. übers. Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Diffusionsgleichung (DE-588)4149816-1 gnd rswk-swf Diffusionsgleichung (DE-588)4149816-1 s DE-604 Wärmeleitungsgleichung (DE-588)4188859-5 s Mathematische Physik (DE-588)4037952-8 s Translations of mathematical monographs 114 (DE-604)BV000002394 114 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004589699&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Itô, Seizô Diffusion equations Translations of mathematical monographs Wärmeleitungsgleichung (DE-588)4188859-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Diffusionsgleichung (DE-588)4149816-1 gnd |
| subject_GND | (DE-588)4188859-5 (DE-588)4037952-8 (DE-588)4149816-1 |
| title | Diffusion equations |
| title_alt | Kakusan-hōteishiki |
| title_auth | Diffusion equations |
| title_exact_search | Diffusion equations |
| title_full | Diffusion equations Seizô Itô |
| title_fullStr | Diffusion equations Seizô Itô |
| title_full_unstemmed | Diffusion equations Seizô Itô |
| title_short | Diffusion equations |
| title_sort | diffusion equations |
| topic | Wärmeleitungsgleichung (DE-588)4188859-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Diffusionsgleichung (DE-588)4149816-1 gnd |
| topic_facet | Wärmeleitungsgleichung Mathematische Physik Diffusionsgleichung |
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