Partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1982
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Applied mathematical sciences
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 249 S. graph. Darst. |
| ISBN: | 0387906096 3540906096 |
Internformat
MARC
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| 100 | 1 | |a John, Fritz |d 1910-1994 |e Verfasser |0 (DE-588)119540053 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations |c Fritz John |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1982 | |
| 300 | |a X, 249 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 1 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Equations différentielles |2 ram | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
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Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 540 J65(4) |
| DE-BY-FWS_katkey | 673863 |
| DE-BY-FWS_media_number | 083000519439 |
| _version_ | 1806182568192638976 |
| adam_text | Contents
Chapter 1
The Single First Order Equation 1
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 2
Second Order Equations: Hyperbolic Equations
for Functions of Two Independent Variables 33
1. Characteristics for Linear and Quasi linear Second order
Equations 33
2. Propagation of Singularities 35
3. The Linear Second Order Equation 37
Problems 39
4. The One Dimensional Wave Equation 40
Problems 45
vii
viii Contents
5. Systems of First Order Equations 46
6. A Quasi linear System and Simple Waves 52
Problem 53
Chapter 3
Characteristic Manifolds and the Cauchy Problem 54
1. Notation of Laurent Schwartz 54
Problems 55
2. The Cauchy Problem 56
Problems 61
3. Real Analytic Functions and the Cauchy Kowalevski Theorem 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. The Lagrange Green Identity 79
5. The Uniqueness Theorem of Holmgren 80
Problems 88
6. Distribution Solutions 89
Problems 92
Chapter 4
The Laplace Equation 94
1. Green s Identity, Fundamental Solutions, and Poisson s Equation 94
Problems . 101
2. The Maximum Principle 103
Problems 105
3. The Dirichlet Problem, Green s Function, and Poisson s Formula 106
Problems 110
4. Proof of Existence of Solutions for the Dirichlet Problem Using
Subharmonic Functions ( Perron s Method ) 111
Problems 116
5. Solution of the Dirichlet Problem by Hilbert Space Methods 117
Problems 125
Chapter 5
Hyperbolic Equations in Higher Dimensions 126
1. The Wave Equation in H Dimensional Space 126
(a) The method of spherical means 126
Problems 132
(b) Hadamard s method of descent 133
Problems 134
Contents ix
(c) Duhamel s principle and the general Cauchy problem 135
Problem 139
(d) Initial boundary value problems ( Mixed problems) 139
Problems 142
2. Higher Order Hyperbolic Equations with Constant Coefficients 143
(a) Standard form of the initial value problem 143
Problem 145
(b) Solution by Fourier transformation 145
Problems 156
(c) Solution of a mixed problem by Fourier transformation 157
(d) The method of plane waves 158
Problems 161
3. Symmetric Hyperbolic Systems 163
(a) The basic energy inequality 163
Problems 169
(b) Existence of solutions by the method of finite differences 172
Problems 181
(c) Existence of solutions by the method of approximation by analytic
functions (Method of Schauder) 182
Chapter 6
Higher Order Elliptic Equations with Constant
Coefficients i85
1. The Fundamental Solution for Odd n 186
Problems 188
2. The Dirichlet Problem 190
Problems 195
3. More on the Hilbert Space //g and the Assumption of Boundary Values in
the Dirichlet Problem 198
Problems 201
Chapter 7
Parabolic Equations 206
1. The Heat Equation 206
(a) The initial value problem 206
Problems 213
(b) Maximum principle, uniqueness, and regularity 215
Problem 220
(c) A mixed problem 220
Problems 221
(d) Non negative solutions 222
Problems 226
2. 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
x Contents
Chapter 8
H. Lewy s Example of a Linear Equation
without Solutions 235
Problems 239
Bibliography 241
Glossary 243
Index 245
|
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| author | John, Fritz 1910-1994 |
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| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)7876733 (DE-599)BVBBV002140474 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515.3/53 510 |
| dewey-search | 515.3/53 510 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| genre | 1\p (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV002140474 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T12:58:45Z |
| institution | BVB |
| isbn | 0387906096 3540906096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001403830 |
| oclc_num | 7876733 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-384 DE-703 DE-739 DE-20 DE-29T DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 DE-706 DE-862 DE-BY-FWS |
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| physical | X, 249 S. graph. Darst. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spellingShingle | John, Fritz 1910-1994 Partial differential equations Applied mathematical sciences Equations différentielles ram Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| 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_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 | Equations différentielles ram Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Equations différentielles Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001403830&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT johnfritz partialdifferentialequations |
Inhaltsverzeichnis
Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 540 J65(4) |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |