The boundary value problems of mathematical physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2010
|
| Ausgabe: | [softcover ed.] |
| Schriftenreihe: | Applied mathematical sciences
49 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XXIII, 322 S. |
| ISBN: | 1441928243 9781441928245 |
Internformat
MARC
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| 240 | 1 | 0 | |a Kraevye zadači matematičeskoj fisiki |
| 245 | 1 | 0 | |a The boundary value problems of mathematical physics |c O. A. Ladyzhenskaya |
| 250 | |a [softcover ed.] | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a XXIII, 322 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Applied mathematical sciences |v 49 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction
xi
Basic Notation xxv
CHAPTER I
Preliminary Considerations
1
§1.
Normed Spaces and Hubert Spaces
1
§2.
Some Properties of Linear Functionals and Bounded Linear Operators
in
Hubert
Space
5
§3.
Unbounded Operators
8
§4.
Generalized Derivatives and Averages
12
§5.
Definition of the Spaces W^Q) and
#ί,(Ω)
19
§6.
The Spaces
&ί(Ω)
and
Ψ (Ω)
and Their Basic Properties
23
§7.
Multiplicative Inequalities for Elements of
W
ί(Ω)
and
»1(Ω)
34
§8.
Embedding Theorems for the Spaces ft JQ) and WlJ£l)
38
Supplements and Problems
41
CHAPTER II
Equations of Elliptic Type
44
§1.
Posing of Boundary Value Problems. Description of the Basic
Material of the Chapter
44
§2.
Generalized Solutions in W (fl). The First (Energy) Inequality
47
§3.
Solvability of the Dirichlet Problem in the Space
»1(Ω).
Three
Theorems of
Fredholm
50
§4.
Expansion in Eigenfunctions of Symmetric Operators
58
§5.
The Second and Third Boundary Value Problems
61
§6.
The Second Fundamental Inequality for Elliptic Operators
64
§7.
Solvability of the Dirichlet Problem in W ifl)
71
§8.
Approximate Methods of Solving Boundary Value Problems
77
Supplements and Problems
85
Contents
CHAPTER
III
Equations of Parabolic Type
03
§1.
Posing Initial-Boundary Value Problems and the Cauchy Problem
104
§2.
First Initial-Boundary Value Problem for the Heat Equation
108
§3.
First Initial-Boundary Value Problem for General Parabolic Equations
116
§4.
Other Boundary Value Problems. The Method of Fourier and
Laplace. The Second Fundamental Inequality
121
§5.
The Method of Rothe 135
Supplements and Problems
139
CHAPTER IV
Equations of Hyperbolic Type
147
§1.
General Considerations. Posing the Fundamental Problems
147
§2.
The Energy Inequality. Finiteness of the Speed of Propagation of
Perturbations. Uniqueness Theorem for Solutions in W
150
§3.
The First Initial-Boundary Value Problem. Solvability in W (QT)
156
§4.
On the Smoothness of Generalized Solutions
161
§5.
Other Initial-Boundary Value Problems
168
§6.
The Functional Method of Solving Initial-Boundary Value Problems
170
§7.
The Methods of Fourier and Laplace
174
Supplements and Problems
181
CHAPTER V
Some Generalizations
183
§1.
Elliptic Equations of Arbitrary Order. Strongly Elliptic Systems
183
§2.
Strongly Parabolic and Strongly Hyperbolic Systems
191
§3. Schrödinger-Type
Equations and Related Equations
194
§4.
Diffraction Problems
196
Supplements and Problems
201
CHAPTER VI
The Method of Finite Differences
212
§1.
General Description of the Method. Some Principles of Constructing
Convergent Difference Schemes
212
§2.
The Fundamental Difference Operators and Their Properties
219
§3.
Interpolations of Grid Functions. The Elementary Embedding Theorems
223
§4.
General Embedding Theorems
230
§5.
The Finite-Difference Method of Fourier
236
§6.
The Elementary Equations
241
§7.
The Dirichlet Problem for General Elliptic Equations of Second Order
261
§8.
The Neumann Problem and Third Boundary Value Problem for
Elliptic Equations
266
§9.
Equations of Parabolic Type
271
§10.
Equations of Hyperbolic Type
281
§11.
Strong Convergence, Systems, Diffraction Problems
294
§12.
Approximation Methods
302
Supplements and Problems
305
Bibliography
309
Index
321
|
| any_adam_object | 1 |
| author | Ladyženskaja, Olʹga A. 1922-2004 |
| author_GND | (DE-588)124284655 |
| author_facet | Ladyženskaja, Olʹga A. 1922-2004 |
| author_role | aut |
| author_sort | Ladyženskaja, Olʹga A. 1922-2004 |
| author_variant | o a l oa oal |
| building | Verbundindex |
| bvnumber | BV039159397 |
| classification_rvk | SK 560 SK 920 SK 950 |
| classification_tum | PHY 013f MAT 350f MAT 354f |
| ctrlnum | (OCoLC)745526545 (DE-599)BVBBV039159397 |
| discipline | Physik Mathematik |
| edition | [softcover ed.] |
| format | Book |
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| id | DE-604.BV039159397 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:00:17Z |
| institution | BVB |
| isbn | 1441928243 9781441928245 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024176937 |
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| physical | XXIII, 322 S. |
| publishDate | 2010 |
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| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Ladyženskaja, Olʹga A. 1922-2004 Verfasser (DE-588)124284655 aut Kraevye zadači matematičeskoj fisiki The boundary value problems of mathematical physics O. A. Ladyzhenskaya [softcover ed.] New York [u.a.] Springer 2010 XXIII, 322 S. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 49 Aus d. Russ. übers. Übers. aus dem Russ. Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Randwertproblem (DE-588)4048395-2 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Applied mathematical sciences 49 (DE-604)BV000005274 49 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024176937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ladyženskaja, Olʹga A. 1922-2004 The boundary value problems of mathematical physics Applied mathematical sciences Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4044779-0 (DE-588)4037952-8 |
| title | The boundary value problems of mathematical physics |
| title_alt | Kraevye zadači matematičeskoj fisiki |
| title_auth | The boundary value problems of mathematical physics |
| title_exact_search | The boundary value problems of mathematical physics |
| title_full | The boundary value problems of mathematical physics O. A. Ladyzhenskaya |
| title_fullStr | The boundary value problems of mathematical physics O. A. Ladyzhenskaya |
| title_full_unstemmed | The boundary value problems of mathematical physics O. A. Ladyzhenskaya |
| title_short | The boundary value problems of mathematical physics |
| title_sort | the boundary value problems of mathematical physics |
| topic | Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Randwertproblem Partielle Differentialgleichung Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024176937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
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