Applications of symmetry methods to partial differential equations:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2010
|
| Schriftenreihe: | Applied mathematical sciences
168 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Angekündigt als: Advanced symmetry method differential equations |
| Beschreibung: | xix, 398 Seiten Diagramme |
| ISBN: | 9780387986128 9780387680286 |
Internformat
MARC
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| 020 | |a 9780387680286 |c eISBN |9 978-0-387-68028-6 | ||
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| 035 | |a (DE-599)BVBBV035876427 | ||
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| 100 | 1 | |a Bluman, George W. |d 1943- |0 (DE-588)143539035 |4 aut | |
| 245 | 1 | 0 | |a Applications of symmetry methods to partial differential equations |c George W. Bluman ; Alexei F. Cheviakov ; Stephen C. Anco |
| 246 | 1 | 3 | |a Advanced symmetry method differential equations |
| 264 | 1 | |a New York, NY |b Springer |c 2010 | |
| 300 | |a xix, 398 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 168 | |
| 500 | |a Angekündigt als: Advanced symmetry method differential equations | ||
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Partial |x Numerical solutions | |
| 650 | 4 | |a Symmetry (Physics) | |
| 650 | 0 | 7 | |a Lie-Gruppe |0 (DE-588)4035695-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Cheviakov, Alexei F. |d 1977- |0 (DE-588)1275326986 |4 aut | |
| 700 | 1 | |a Anco, Stephen C. |0 (DE-588)1275327133 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-68028-6 |
| 830 | 0 | |a Applied mathematical sciences |v 168 |w (DE-604)BV000005274 |9 168 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805071956252295168 |
|---|---|
| adam_text |
Contents
Preface
. ix
Introduction
. xiii
1
Local Transformations and Conservation
Laws
. 1
1.1
Introduction
. 1
1.2
Local Transformations
. 5
1.2.1
Point transformations
. 6
1.2.2
Contact transformations
. 8
1.2.3
Higher-order
transformations
. 10
1.2.4
One-parameter higher-order
transformations
. 10
1.2.5
Point
symmetries
. IG
1.2.6
Contact
and higher-order symmetries.
20
1.2.7
Equivalence
transformations and symmetry
classification
. 21
1.2.8
Recursion operators
for local
symmetries
. 24
1.3
Conservation
Laws
. 38
1.3.1
Local conservation
laws.
38
1.3.2
Equivalent conservation
laws
. 42
1.3.3
Multipliers for
conservation
laws.
Euler operators
. 43
1.3.4
The direct method for construction of conservation
laws. Cauchy-Kovalevskaya form
. 46
1.3.5
Examples
. 50
1.3.6
Linearizing operators and adjoint equations
. 53
1.3.7
Determination of fluxes of conservation laws from
multipliers
. 56
1.3.8
Self-adjoint PDE systems
. 64
1.4
Noether's
Theorem
. 70
1.4.1
Euler-Lagrange equations
. 71
1.4.2
Noether's formulation of Noether's theorem
. 72
vj Contents
1.4.3
Boyer's
formulation of Noether's theorem
. 75
1.4.4
Limitations of Noether's theorem
. 77
1.4.5
Examples
. 79
1.5
Some Connections Between Symmetries and Conservation
Laws
.". 89
1.5.1
Use of symmetries to find new conservation laws from
known conservation laws
. 90
1.5.2
Relationships among symmetries, solutions of adjoint
equations, and conservation laws
.107
1.6
Discussion
.
П7
2
Construction of Mappings Relating Differential Equations
121
2.1
Introduction
.121
2.2
Notations; Mappings of Infinitesimal Generators
.123
2.2.1
Theorems on
invertitile
mappings
.127
2.3
Mapping of a Given PDE to a Specific Target PDE
.128
2.3.1
Construction of non-invertible mappings
.129
2.3.2
Construction of an invertible mapping by a point
transformation
.133
2.4
Invertible Mappings of Nonlinear PDEs to Linear PDEs
Through Symmetries
.139
2.4.1
Invertible mappings of nonlinear PDE systems (with
at least two dependent variables) to linear PDE systems
141
2.4.2
Invertible mappings of nonlinear PDE systems (with
one dependent variable) to linear PDE systems
.
14fi
2.5
Invertible Mappings of Linear PDEs to Linear PDEs with
Constant Coefficients
.158
2.5.1
Examples of mapping variable coefficient linear PDEs
to constant coefficient linear PDEs through invertible
point transformations
.163
2.5.2
Example of finding the most general mapping of
a given constant coefficient linear PDE to some
constant coefficient linear PDE
.168
2.6
Invertible Mappings of Nonlinear PDEs to Linear PDEs
Through Conservation Law Multipliers
.173
2.6.1
Computational steps
.177
2.6.2
Examples of linearizations of nonlinear PDEs through
conservation law multipliers
.179
2.7
Discussion
.184
3
Nonlocally Related PDE Systems
.187
3.1
Introduction
.187
Contents
vu
3.2 Noniocally
Related
Potential Systems and Subsystems in
Two Dimensions.
191
3.2.1 Potential
systems.
192
3.2.2
Noniocally
related subsystems
.193
3.3
Trees of
Noniocally
Related PDE Systems
.199
3.3.1
Basic procedure of tree construction
.200
3.3.2
A tree for a nonlinear diffusion equation
.202
3.3.3
A tree for planar gas dynamics (PGD) equations
.204
3.4
Nonlocal Conservation Laws
.209
3.4.1
Conservation laws arising from
noniocally
related
systems
.210
3.4.2
Nonlocal conservation laws for diffusion-convection
equations
.212
3.4.3
Additional conservation laws of nonlinear telegraph
equations
.214
3.5
Extended Tree Construction Procedure
.222
3.5.1
An extended tree construction procedure
.223
3.5.2
An extended tree for a nonlinear diffusion equation
. 225
3.5.3
An extended tree for a nonlinear wave equation
.228
3.5.4
An extended tree for the planar gas dynamics equations232
3.6
Discussion
.242
4
Applications of Noniocally Related PDE Systems
.245
4.1
Introduction
.245
4.2
Nonlocal Symmetries
.248
4.2.1
Nonlocal symmetries of a nonlinear diffusion equation
. 251
4.2.2
Nonlocal symmetries of a nonlinear wave equation
. 256
4.2.3
Classification of nonlocal symmetries of nonlinear
telegraph equations arising from point symmetries of
potential systems
.270
4.2.4
Nonlocal symmetries of nonlinear telegraph equations
with power law nonlinearities
.271
4.2.5
Nonlocal symmetries of the planar gas dynamics
equations
.270
4.3
Construction of Non-invertible Mappings Relating PDEs
. 283
4.3.1
Non-invertible mappings of nonlinear PDE systems
to linear PDE systems
. 284
4.3.2
Non-invertible mappings of linear PDEs with variable
coefficients to linear PDEs with constant coefficients
. . 290
4.4
Discussion
. 294
vin
Contents
5
Further Applications of Symmetry Methods:
Miscellaneous Extensions
.297
5.1
Introduction
.297
5.2
Applications of Symmetry Methods to the Construction of
Solutions of PDEs
.301
5.2.1
The classical method
.302
5.2.2
The nonclassical method
.306
5.2.3
Invariant solutions arising from nonlocal symmetries
that are local symmetries of nonlocally related systems
314
5.2.4
Further extensions of symmetry methods for
construction of solutions of PDEs connected with
nonlocally related systems
.320
5.3
Nonlocally Related PDE Systems in Three or More
Dimensions
.333
5.3.1
Divergence-type conservation laws and resulting
potential systems
.334
5.3.2
Nonlocally related subsystems
.336
5.3.3
Tree construction, nonlocal conservation laws, and
nonlocal symmetries
.337
5.3.4
Lower-degree conservation laws and related potential
systems
.341
5.3.5
Examples of applications of nonlocally related
systems in higher dimensions
.343
5.3.6
Symmetries and exact solutions of the three-
dimensional
MHD
equilibrium equations
.350
5.4
Symbolic Software
.357
5.4.1
An example of symbolic computation of point
symmetries
.357
5.4.2
An example of point symmetry classification
.359
5.4.3
An example of symbolic computation of conservation
laws
.363
5.5
Discussion
.364
References
.369
Theorem, Corollary and Lemma Index
.383
Author Index
.385
Subject Index
.389 |
| any_adam_object | 1 |
| author | Bluman, George W. 1943- Cheviakov, Alexei F. 1977- Anco, Stephen C. |
| author_GND | (DE-588)143539035 (DE-588)1275326986 (DE-588)1275327133 |
| author_facet | Bluman, George W. 1943- Cheviakov, Alexei F. 1977- Anco, Stephen C. |
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| author_sort | Bluman, George W. 1943- |
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| classification_rvk | SK 540 SK 920 |
| ctrlnum | (OCoLC)495771242 (DE-599)BVBBV035876427 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035876427 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:46:03Z |
| institution | BVB |
| isbn | 9780387986128 9780387680286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018734101 |
| oclc_num | 495771242 |
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| physical | xix, 398 Seiten Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Bluman, George W. 1943- (DE-588)143539035 aut Applications of symmetry methods to partial differential equations George W. Bluman ; Alexei F. Cheviakov ; Stephen C. Anco Advanced symmetry method differential equations New York, NY Springer 2010 xix, 398 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 168 Angekündigt als: Advanced symmetry method differential equations Differential equations Numerical solutions Differential equations, Partial Numerical solutions Symmetry (Physics) Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s Lie-Gruppe (DE-588)4035695-4 s DE-604 Cheviakov, Alexei F. 1977- (DE-588)1275326986 aut Anco, Stephen C. (DE-588)1275327133 aut Erscheint auch als Online-Ausgabe 978-0-387-68028-6 Applied mathematical sciences 168 (DE-604)BV000005274 168 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bluman, George W. 1943- Cheviakov, Alexei F. 1977- Anco, Stephen C. Applications of symmetry methods to partial differential equations Applied mathematical sciences Differential equations Numerical solutions Differential equations, Partial Numerical solutions Symmetry (Physics) Lie-Gruppe (DE-588)4035695-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4044779-0 (DE-588)4128130-5 |
| title | Applications of symmetry methods to partial differential equations |
| title_alt | Advanced symmetry method differential equations |
| title_auth | Applications of symmetry methods to partial differential equations |
| title_exact_search | Applications of symmetry methods to partial differential equations |
| title_full | Applications of symmetry methods to partial differential equations George W. Bluman ; Alexei F. Cheviakov ; Stephen C. Anco |
| title_fullStr | Applications of symmetry methods to partial differential equations George W. Bluman ; Alexei F. Cheviakov ; Stephen C. Anco |
| title_full_unstemmed | Applications of symmetry methods to partial differential equations George W. Bluman ; Alexei F. Cheviakov ; Stephen C. Anco |
| title_short | Applications of symmetry methods to partial differential equations |
| title_sort | applications of symmetry methods to partial differential equations |
| topic | Differential equations Numerical solutions Differential equations, Partial Numerical solutions Symmetry (Physics) Lie-Gruppe (DE-588)4035695-4 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential equations Numerical solutions Differential equations, Partial Numerical solutions Symmetry (Physics) Lie-Gruppe Partielle Differentialgleichung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
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