Partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
[1999]
|
| Ausgabe: | 4. ed., [repr.] |
| Schriftenreihe: | Applied mathematical sciences
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 249 S. graph. Darst. |
| ISBN: | 0387906096 3540906096 |
Internformat
MARC
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| 100 | 1 | |a John, Fritz |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations |c Fritz John |
| 250 | |a 4. ed., [repr.] | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c [1999] | |
| 300 | |a X, 249 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Applied mathematical sciences |v 1 | |
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Datensatz im Suchindex
| _version_ | 1804136557189267456 |
|---|---|
| adam_text | Contents
Chapter I
The Single First-Order Equation
1.
Introduction
1
2.
Examples
2
3.
Analytic Solution and Approximation Methods in a Simple
Example
4
Problems
8
4.
Quasi-linear Equations
9
5.
The Cauchy Problem for the Quasi-linear Equation
11
6.
Examples
15
Problems
18
7.
The General First-Order Equation for a Function of Two
Variables
19
8.
The Cauchy Problem
24
9.
Solutions Generated as Envelopes
29
Problems
31
Chapter
Second-Order Equations
for Functions of Two Independent Variables
1.
Equations
2.
3.
Problems
4.
Problems
vii
viii Contents
5.
6.
Problem
Chapter
Characteristic Manifolds and the Cauchy Problem
1.
54
Problems
55
2.
56
Problems
61
3.
61
(a) Multiple infinite series
62
Problems
63
(b) Real analytic functions
64
Problems
69
(c) Analytic and real analytic functions
70
Problems
72
(d) The proof of the Cauchy-Kowalevski theorem
73
Problems
78
4.
79
5.
80
Problems
88
6.
89
Problems
92
Chapter
The Laplace Equation
94
1.
94
Problems
101
2.
103
Problems
105
3.
106
Problems
110
4.
Subharmonic Functions ( Perron s Method )
111
Problems
116
5.
117
Problems
125
Chapter
Hyperbolic Equations in Higher Dimensions
126
1.
126
(a) The method of spherical means
126
Problems
132
(b) Hadamard s method of descent
133
Problems
134
Contents ix
(c) Duhameľs
Problem
(d) Initial-boundary-value problems ( Mixed problems)
Problems
2.
(a) Standard form of the initial-value problem
Problem
(b) Solution by Fourier transformation
Problems
(c) Solution of a mixed problem by Fourier transformation
(d) The method of plane waves
Problems
3.
(a) The basic energy inequality
Problems
(b) Existence of solutions by the method of finite differences
Problems
(c) Existence of solutions by the method of approximation by analytic
functions (Method of
Chapter
Higher-Order Elliptic Equations with Constant
Coefficients
1.
Problems
2.
Problems
3.
the Dirichiet Problem
Problems
Chapter
Parabolic Equations 206
2.
The Heat Equation
206
(a) The initial-value problem
206
Problems
213
(b) Maximum principle, uniqueness, and regularity
215
Problem
220
(c) A
220
Problems
221
(d) Non-negative solutions
222
Problems
226
The Initial-Value Problem for General Second-Order Linear
Parabolic Equations
227
(a) The method of finite differences and the maximum principle
227
(b) Existence of solutions of the initial-value problem
231
Problems
233
χ
Chapter
Η.
without Solutions
Problems
Bibliography
Glossary
Index
|
| adam_txt |
Contents
Chapter I
The Single First-Order Equation
1.
Introduction
1
2.
Examples
2
3.
Analytic Solution and Approximation Methods in a Simple
Example
4
Problems
8
4.
Quasi-linear Equations
9
5.
The Cauchy Problem for the Quasi-linear Equation
11
6.
Examples
15
Problems
18
7.
The General First-Order Equation for a Function of Two
Variables
19
8.
The Cauchy Problem
24
9.
Solutions Generated as Envelopes
29
Problems
31
Chapter
Second-Order Equations
for Functions of Two Independent Variables
1.
Equations
2.
3.
Problems
4.
Problems
vii
viii Contents
5.
6.
Problem
Chapter
Characteristic Manifolds and the Cauchy Problem
1.
54
Problems
55
2.
56
Problems
61
3.
61
(a) Multiple infinite series
62
Problems
63
(b) Real analytic functions
64
Problems
69
(c) Analytic and real analytic functions
70
Problems
72
(d) The proof of the Cauchy-Kowalevski theorem
73
Problems
78
4.
79
5.
80
Problems
88
6.
89
Problems
92
Chapter
The Laplace Equation
94
1.
94
Problems
101
2.
103
Problems
105
3.
106
Problems
110
4.
Subharmonic Functions ("Perron's Method")
111
Problems
116
5.
117
Problems
125
Chapter
Hyperbolic Equations in Higher Dimensions
126
1.
126
(a) The method of spherical means
126
Problems
132
(b) Hadamard's method of descent
133
Problems
134
Contents ix
(c) Duhameľs
Problem
(d) Initial-boundary-value problems ("Mixed" problems)
Problems
2.
(a) Standard form of the initial-value problem
Problem
(b) Solution by Fourier transformation
Problems
(c) Solution of a mixed problem by Fourier transformation
(d) The method of plane waves
Problems
3.
(a) The basic energy inequality
Problems
(b) Existence of solutions by the method of finite differences
Problems
(c) Existence of solutions by the method of approximation by analytic
functions (Method of
Chapter
Higher-Order Elliptic Equations with Constant
Coefficients
1.
Problems
2.
Problems
3.
the Dirichiet Problem
Problems
Chapter
Parabolic Equations 206
2.
The Heat Equation
206
(a) The initial-value problem
206
Problems
213
(b) Maximum principle, uniqueness, and regularity
215
Problem
220
(c) A
220
Problems
221
(d) Non-negative solutions
222
Problems
226
The Initial-Value Problem for General Second-Order Linear
Parabolic Equations
227
(a) The method of finite differences and the maximum principle
227
(b) Existence of solutions of the initial-value problem
231
Problems
233
χ
Chapter
Η.
without Solutions
Problems
Bibliography
Glossary
Index |
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| index_date | 2024-07-02T17:44:18Z |
| indexdate | 2024-07-09T20:58:17Z |
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| isbn | 0387906096 3540906096 |
| language | English |
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| spelling | John, Fritz Verfasser aut Partial differential equations Fritz John 4. ed., [repr.] New York [u.a.] Springer [1999] X, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 1 Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift gnd-content Partielle Differentialgleichung (DE-588)4044779-0 s 2\p DE-604 Applied mathematical sciences 1 (DE-604)BV000005274 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015677711&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| subject_GND | (DE-588)4044779-0 (DE-588)1071861417 |
| title | Partial differential equations |
| title_auth | Partial differential equations |
| title_exact_search | Partial differential equations |
| title_exact_search_txtP | Partial differential equations |
| title_full | Partial differential equations Fritz John |
| title_fullStr | Partial differential equations Fritz John |
| title_full_unstemmed | Partial differential equations Fritz John |
| title_short | Partial differential equations |
| title_sort | partial differential equations |
| topic | Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partielle Differentialgleichung Konferenzschrift |
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