Lie's structural approach to PDE systems /:
This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The b...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
2000.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 80. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields. |
| Beschreibung: | 1 online resource (xv, 572 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107089426 1107089425 9780511569456 0511569459 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn852899174 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130716s2000 nyu ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d CAMBR |d IDEBK |d E7B |d OCLCF |d OCLCQ |d AGLDB |d YDX |d OCLCQ |d HEBIS |d OCLCO |d COO |d VTS |d STF |d AU@ |d M8D |d UKAHL |d OCLCQ |d K6U |d INARC |d SFB |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d OCLCQ | ||
| 019 | |a 841393163 | ||
| 020 | |a 9781107089426 |q (electronic bk.) | ||
| 020 | |a 1107089425 |q (electronic bk.) | ||
| 020 | |a 9780511569456 |q (electronic bk.) | ||
| 020 | |a 0511569459 |q (electronic bk.) | ||
| 020 | |z 0521780888 | ||
| 020 | |z 9780521780889 | ||
| 035 | |a (OCoLC)852899174 |z (OCoLC)841393163 | ||
| 050 | 4 | |a QA377 |b .S846 2000eb | |
| 072 | 7 | |a MAT |x 007020 |2 bisacsh | |
| 082 | 7 | |a 515/.353 |2 22 | |
| 084 | |a 31.45 |2 bcl | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Stormark, Olle, |d 1945- |1 https://id.oclc.org/worldcat/entity/E39PCjDk3jHycWR8TvYMkrhyMK |0 http://id.loc.gov/authorities/names/n99830835 | |
| 245 | 1 | 0 | |a Lie's structural approach to PDE systems / |c Olle Stormark. |
| 260 | |a New York : |b Cambridge University Press, |c 2000. | ||
| 300 | |a 1 online resource (xv, 572 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v 80 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields. | ||
| 505 | 0 | |a Cover; Half Title; Series Page; Title; Copyright; Contents; Preface; 1 Introduction and summary; 2 PDE systems, pfaffian systems and vector field systems; 2.1 ODE systems, vector fields and 1-parameter groups; 2.2 First order PDE systems in one dependent variable, pfaffian equations and contact transformations; 2.3 Jet bundles and contact pfaffian systems; 2.4 The theorem of Frobenius; 2.5 Mayer's blowing-up method for proving the Frobenius theorem; 3 Cartan's local existence theorem; 3.1 Involutions and characters; 3.2 From involutions to complete systems | |
| 505 | 8 | |a 3.3 How general is the general solution?3.4 Cauchy characteristics; 3.5 Maximal involutions and integrable vector field systems; 4 Involutivity and the prolongation theorem; 4.1 Independence condition and involutivity; 4.2 Prolongations; 4.3 Explanation of the prolongation theorem; 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics; 5.1 The classification of Drach; 5.2 Second order PDEs in one unknown and their singular vector fields; 5.3 Monge characteristic subsystems; 6 Integration of vector field systems V satisfying dim V' = dim V +1 | |
| 505 | 8 | |a 6.1 Maximal involutions6.2 Complete subsystems; 6.3 The generalized contact bracket; 6.4 Reduction to a canonical form and systems of contact coordinates; 6.5 How to find all maximal complete subsystems of V; 6.6 Contact transformations and Lie pseudogroups; 7 Higher order contact transformations; 7.1 Lie's rectification theorem for first order PDE systems in one dependent variable; 7.2 Backlund's theorems; 7.3 Contact prolongations of local diffeomorphisms; 8 Local Lie groups; 8.1 The parameter group and its structure constants; 8.2 The left- and right-invariant parameter groups | |
| 505 | 8 | |a 8.3 Left- and right-invariant vector fields and their dual Maurer-Cartan forms8.4 One-parameter subgroups and the exponential mapping; 8.5 The first and second fundamental theorems; 8.6 The third fundamental theorem; 8.7 Local transformation groups; 9 Structural classification of 3-dimensional Lie algebras over the complex numbers; 9.1 The classification; 9.2 Realizations as transformation groups; 10 Lie equations and Lie vector field systems; 10.1 Characterization of ODE systems with fundamental solutions; 10.2 Lie vector field systems associated to Lie groups | |
| 505 | 8 | |a 11 Second order PDEs in one dependent and two independent variables11.1 Second order PDEs and associated vector field systems; 11.2 Monge systems; 11.3 A connection with line geometry; 11.4 Darboux's method for hyperbolic PDEs; 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals; 12.1 First integrals of the first order; 12.2 Two first integrals for each Monge system; 12.3 How to find integral manifolds; 12.4 Integrable systems; 12.5 Two first integrals for one Monge system and three for the other; 12.6 Three first integrals for each Monge system | |
| 650 | 0 | |a Differential equations, Partial |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85037915 | |
| 650 | 6 | |a Équations aux dérivées partielles |x Solutions numériques. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Partial |x Numerical solutions |2 fast | |
| 650 | 7 | |a Lie-Algebra |2 gnd |0 http://d-nb.info/gnd/4130355-6 | |
| 650 | 7 | |a Partielle Differentialgleichung |2 gnd |0 http://d-nb.info/gnd/4044779-0 | |
| 650 | 1 | 7 | |a Partiële differentiaalvergelijkingen. |2 gtt |
| 650 | 1 | 7 | |a Lie-groepen. |2 gtt |
| 650 | 7 | |a Équations aux dérivées partielles |x Analyse numérique. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Stormark, Olle, 1945- |t Lie's structural approach to PDE systems. |d New York : Cambridge University Press, 2000 |z 0521780888 |w (DLC) 99054436 |w (OCoLC)42752834 |
| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v v. 80. |0 http://id.loc.gov/authorities/names/n42010632 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569323 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26385530 | ||
| 938 | |a ebrary |b EBRY |n ebr10733679 | ||
| 938 | |a EBSCOhost |b EBSC |n 569323 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis26006586 | ||
| 938 | |a Internet Archive |b INAR |n liesstructuralap0000stor | ||
| 938 | |a YBP Library Services |b YANK |n 10440722 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn852899174 |
|---|---|
| _version_ | 1816882238586880000 |
| adam_text | |
| any_adam_object | |
| author | Stormark, Olle, 1945- |
| author_GND | http://id.loc.gov/authorities/names/n99830835 |
| author_facet | Stormark, Olle, 1945- |
| author_role | |
| author_sort | Stormark, Olle, 1945- |
| author_variant | o s os |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 .S846 2000eb |
| callnumber-search | QA377 .S846 2000eb |
| callnumber-sort | QA 3377 S846 42000EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Half Title; Series Page; Title; Copyright; Contents; Preface; 1 Introduction and summary; 2 PDE systems, pfaffian systems and vector field systems; 2.1 ODE systems, vector fields and 1-parameter groups; 2.2 First order PDE systems in one dependent variable, pfaffian equations and contact transformations; 2.3 Jet bundles and contact pfaffian systems; 2.4 The theorem of Frobenius; 2.5 Mayer's blowing-up method for proving the Frobenius theorem; 3 Cartan's local existence theorem; 3.1 Involutions and characters; 3.2 From involutions to complete systems 3.3 How general is the general solution?3.4 Cauchy characteristics; 3.5 Maximal involutions and integrable vector field systems; 4 Involutivity and the prolongation theorem; 4.1 Independence condition and involutivity; 4.2 Prolongations; 4.3 Explanation of the prolongation theorem; 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics; 5.1 The classification of Drach; 5.2 Second order PDEs in one unknown and their singular vector fields; 5.3 Monge characteristic subsystems; 6 Integration of vector field systems V satisfying dim V' = dim V +1 6.1 Maximal involutions6.2 Complete subsystems; 6.3 The generalized contact bracket; 6.4 Reduction to a canonical form and systems of contact coordinates; 6.5 How to find all maximal complete subsystems of V; 6.6 Contact transformations and Lie pseudogroups; 7 Higher order contact transformations; 7.1 Lie's rectification theorem for first order PDE systems in one dependent variable; 7.2 Backlund's theorems; 7.3 Contact prolongations of local diffeomorphisms; 8 Local Lie groups; 8.1 The parameter group and its structure constants; 8.2 The left- and right-invariant parameter groups 8.3 Left- and right-invariant vector fields and their dual Maurer-Cartan forms8.4 One-parameter subgroups and the exponential mapping; 8.5 The first and second fundamental theorems; 8.6 The third fundamental theorem; 8.7 Local transformation groups; 9 Structural classification of 3-dimensional Lie algebras over the complex numbers; 9.1 The classification; 9.2 Realizations as transformation groups; 10 Lie equations and Lie vector field systems; 10.1 Characterization of ODE systems with fundamental solutions; 10.2 Lie vector field systems associated to Lie groups 11 Second order PDEs in one dependent and two independent variables11.1 Second order PDEs and associated vector field systems; 11.2 Monge systems; 11.3 A connection with line geometry; 11.4 Darboux's method for hyperbolic PDEs; 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals; 12.1 First integrals of the first order; 12.2 Two first integrals for each Monge system; 12.3 How to find integral manifolds; 12.4 Integrable systems; 12.5 Two first integrals for one Monge system and three for the other; 12.6 Three first integrals for each Monge system |
| ctrlnum | (OCoLC)852899174 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06899cam a2200685 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn852899174</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">130716s2000 nyu ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">CAMBR</subfield><subfield code="d">IDEBK</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">YDX</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">HEBIS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">COO</subfield><subfield code="d">VTS</subfield><subfield code="d">STF</subfield><subfield code="d">AU@</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">K6U</subfield><subfield code="d">INARC</subfield><subfield code="d">SFB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">841393163</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107089426</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107089425</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511569456</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511569459</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0521780888</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780521780889</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)852899174</subfield><subfield code="z">(OCoLC)841393163</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA377</subfield><subfield code="b">.S846 2000eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">007020</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515/.353</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.45</subfield><subfield code="2">bcl</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stormark, Olle,</subfield><subfield code="d">1945-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjDk3jHycWR8TvYMkrhyMK</subfield><subfield code="0">http://id.loc.gov/authorities/names/n99830835</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lie's structural approach to PDE systems /</subfield><subfield code="c">Olle Stormark.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2000.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xv, 572 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Encyclopedia of mathematics and its applications ;</subfield><subfield code="v">80</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Half Title; Series Page; Title; Copyright; Contents; Preface; 1 Introduction and summary; 2 PDE systems, pfaffian systems and vector field systems; 2.1 ODE systems, vector fields and 1-parameter groups; 2.2 First order PDE systems in one dependent variable, pfaffian equations and contact transformations; 2.3 Jet bundles and contact pfaffian systems; 2.4 The theorem of Frobenius; 2.5 Mayer's blowing-up method for proving the Frobenius theorem; 3 Cartan's local existence theorem; 3.1 Involutions and characters; 3.2 From involutions to complete systems</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.3 How general is the general solution?3.4 Cauchy characteristics; 3.5 Maximal involutions and integrable vector field systems; 4 Involutivity and the prolongation theorem; 4.1 Independence condition and involutivity; 4.2 Prolongations; 4.3 Explanation of the prolongation theorem; 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics; 5.1 The classification of Drach; 5.2 Second order PDEs in one unknown and their singular vector fields; 5.3 Monge characteristic subsystems; 6 Integration of vector field systems V satisfying dim V' = dim V +1</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.1 Maximal involutions6.2 Complete subsystems; 6.3 The generalized contact bracket; 6.4 Reduction to a canonical form and systems of contact coordinates; 6.5 How to find all maximal complete subsystems of V; 6.6 Contact transformations and Lie pseudogroups; 7 Higher order contact transformations; 7.1 Lie's rectification theorem for first order PDE systems in one dependent variable; 7.2 Backlund's theorems; 7.3 Contact prolongations of local diffeomorphisms; 8 Local Lie groups; 8.1 The parameter group and its structure constants; 8.2 The left- and right-invariant parameter groups</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">8.3 Left- and right-invariant vector fields and their dual Maurer-Cartan forms8.4 One-parameter subgroups and the exponential mapping; 8.5 The first and second fundamental theorems; 8.6 The third fundamental theorem; 8.7 Local transformation groups; 9 Structural classification of 3-dimensional Lie algebras over the complex numbers; 9.1 The classification; 9.2 Realizations as transformation groups; 10 Lie equations and Lie vector field systems; 10.1 Characterization of ODE systems with fundamental solutions; 10.2 Lie vector field systems associated to Lie groups</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">11 Second order PDEs in one dependent and two independent variables11.1 Second order PDEs and associated vector field systems; 11.2 Monge systems; 11.3 A connection with line geometry; 11.4 Darboux's method for hyperbolic PDEs; 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals; 12.1 First integrals of the first order; 12.2 Two first integrals for each Monge system; 12.3 How to find integral manifolds; 12.4 Integrable systems; 12.5 Two first integrals for one Monge system and three for the other; 12.6 Three first integrals for each Monge system</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations, Partial</subfield><subfield code="x">Numerical solutions.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037915</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations aux dérivées partielles</subfield><subfield code="x">Solutions numériques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">Partial.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Partial</subfield><subfield code="x">Numerical solutions</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lie-Algebra</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4130355-6</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4044779-0</subfield></datafield><datafield tag="650" ind1="1" ind2="7"><subfield code="a">Partiële differentiaalvergelijkingen.</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1="1" ind2="7"><subfield code="a">Lie-groepen.</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Équations aux dérivées partielles</subfield><subfield code="x">Analyse numérique.</subfield><subfield code="2">ram</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Stormark, Olle, 1945-</subfield><subfield code="t">Lie's structural approach to PDE systems.</subfield><subfield code="d">New York : Cambridge University Press, 2000</subfield><subfield code="z">0521780888</subfield><subfield code="w">(DLC) 99054436</subfield><subfield code="w">(OCoLC)42752834</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Encyclopedia of mathematics and its applications ;</subfield><subfield code="v">v. 80.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42010632</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569323</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH26385530</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10733679</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">569323</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis26006586</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">liesstructuralap0000stor</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10440722</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn852899174 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:26Z |
| institution | BVB |
| isbn | 9781107089426 1107089425 9780511569456 0511569459 |
| language | English |
| oclc_num | 852899174 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 572 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Stormark, Olle, 1945- https://id.oclc.org/worldcat/entity/E39PCjDk3jHycWR8TvYMkrhyMK http://id.loc.gov/authorities/names/n99830835 Lie's structural approach to PDE systems / Olle Stormark. New York : Cambridge University Press, 2000. 1 online resource (xv, 572 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; 80 Includes bibliographical references and index. Print version record. This book provides a lucid and comprehensive introduction to the differential geometric study of partial differential equations. It was the first book to present substantial results on local solvability of general and, in particular, nonlinear PDE systems without using power series techniques. The book describes a general approach to systems of partial differential equations based on ideas developed by Lie, Cartan and Vessiot. The most basic question is that of local solvability, but the methods used also yield classifications of various families of PDE systems. The central idea is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields. Cover; Half Title; Series Page; Title; Copyright; Contents; Preface; 1 Introduction and summary; 2 PDE systems, pfaffian systems and vector field systems; 2.1 ODE systems, vector fields and 1-parameter groups; 2.2 First order PDE systems in one dependent variable, pfaffian equations and contact transformations; 2.3 Jet bundles and contact pfaffian systems; 2.4 The theorem of Frobenius; 2.5 Mayer's blowing-up method for proving the Frobenius theorem; 3 Cartan's local existence theorem; 3.1 Involutions and characters; 3.2 From involutions to complete systems 3.3 How general is the general solution?3.4 Cauchy characteristics; 3.5 Maximal involutions and integrable vector field systems; 4 Involutivity and the prolongation theorem; 4.1 Independence condition and involutivity; 4.2 Prolongations; 4.3 Explanation of the prolongation theorem; 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics; 5.1 The classification of Drach; 5.2 Second order PDEs in one unknown and their singular vector fields; 5.3 Monge characteristic subsystems; 6 Integration of vector field systems V satisfying dim V' = dim V +1 6.1 Maximal involutions6.2 Complete subsystems; 6.3 The generalized contact bracket; 6.4 Reduction to a canonical form and systems of contact coordinates; 6.5 How to find all maximal complete subsystems of V; 6.6 Contact transformations and Lie pseudogroups; 7 Higher order contact transformations; 7.1 Lie's rectification theorem for first order PDE systems in one dependent variable; 7.2 Backlund's theorems; 7.3 Contact prolongations of local diffeomorphisms; 8 Local Lie groups; 8.1 The parameter group and its structure constants; 8.2 The left- and right-invariant parameter groups 8.3 Left- and right-invariant vector fields and their dual Maurer-Cartan forms8.4 One-parameter subgroups and the exponential mapping; 8.5 The first and second fundamental theorems; 8.6 The third fundamental theorem; 8.7 Local transformation groups; 9 Structural classification of 3-dimensional Lie algebras over the complex numbers; 9.1 The classification; 9.2 Realizations as transformation groups; 10 Lie equations and Lie vector field systems; 10.1 Characterization of ODE systems with fundamental solutions; 10.2 Lie vector field systems associated to Lie groups 11 Second order PDEs in one dependent and two independent variables11.1 Second order PDEs and associated vector field systems; 11.2 Monge systems; 11.3 A connection with line geometry; 11.4 Darboux's method for hyperbolic PDEs; 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals; 12.1 First integrals of the first order; 12.2 Two first integrals for each Monge system; 12.3 How to find integral manifolds; 12.4 Integrable systems; 12.5 Two first integrals for one Monge system and three for the other; 12.6 Three first integrals for each Monge system Differential equations, Partial Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037915 Équations aux dérivées partielles Solutions numériques. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial Numerical solutions fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Partiële differentiaalvergelijkingen. gtt Lie-groepen. gtt Équations aux dérivées partielles Analyse numérique. ram Print version: Stormark, Olle, 1945- Lie's structural approach to PDE systems. New York : Cambridge University Press, 2000 0521780888 (DLC) 99054436 (OCoLC)42752834 Encyclopedia of mathematics and its applications ; v. 80. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569323 Volltext |
| spellingShingle | Stormark, Olle, 1945- Lie's structural approach to PDE systems / Encyclopedia of mathematics and its applications ; Cover; Half Title; Series Page; Title; Copyright; Contents; Preface; 1 Introduction and summary; 2 PDE systems, pfaffian systems and vector field systems; 2.1 ODE systems, vector fields and 1-parameter groups; 2.2 First order PDE systems in one dependent variable, pfaffian equations and contact transformations; 2.3 Jet bundles and contact pfaffian systems; 2.4 The theorem of Frobenius; 2.5 Mayer's blowing-up method for proving the Frobenius theorem; 3 Cartan's local existence theorem; 3.1 Involutions and characters; 3.2 From involutions to complete systems 3.3 How general is the general solution?3.4 Cauchy characteristics; 3.5 Maximal involutions and integrable vector field systems; 4 Involutivity and the prolongation theorem; 4.1 Independence condition and involutivity; 4.2 Prolongations; 4.3 Explanation of the prolongation theorem; 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics; 5.1 The classification of Drach; 5.2 Second order PDEs in one unknown and their singular vector fields; 5.3 Monge characteristic subsystems; 6 Integration of vector field systems V satisfying dim V' = dim V +1 6.1 Maximal involutions6.2 Complete subsystems; 6.3 The generalized contact bracket; 6.4 Reduction to a canonical form and systems of contact coordinates; 6.5 How to find all maximal complete subsystems of V; 6.6 Contact transformations and Lie pseudogroups; 7 Higher order contact transformations; 7.1 Lie's rectification theorem for first order PDE systems in one dependent variable; 7.2 Backlund's theorems; 7.3 Contact prolongations of local diffeomorphisms; 8 Local Lie groups; 8.1 The parameter group and its structure constants; 8.2 The left- and right-invariant parameter groups 8.3 Left- and right-invariant vector fields and their dual Maurer-Cartan forms8.4 One-parameter subgroups and the exponential mapping; 8.5 The first and second fundamental theorems; 8.6 The third fundamental theorem; 8.7 Local transformation groups; 9 Structural classification of 3-dimensional Lie algebras over the complex numbers; 9.1 The classification; 9.2 Realizations as transformation groups; 10 Lie equations and Lie vector field systems; 10.1 Characterization of ODE systems with fundamental solutions; 10.2 Lie vector field systems associated to Lie groups 11 Second order PDEs in one dependent and two independent variables11.1 Second order PDEs and associated vector field systems; 11.2 Monge systems; 11.3 A connection with line geometry; 11.4 Darboux's method for hyperbolic PDEs; 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals; 12.1 First integrals of the first order; 12.2 Two first integrals for each Monge system; 12.3 How to find integral manifolds; 12.4 Integrable systems; 12.5 Two first integrals for one Monge system and three for the other; 12.6 Three first integrals for each Monge system Differential equations, Partial Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037915 Équations aux dérivées partielles Solutions numériques. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial Numerical solutions fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Partiële differentiaalvergelijkingen. gtt Lie-groepen. gtt Équations aux dérivées partielles Analyse numérique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037915 http://d-nb.info/gnd/4130355-6 http://d-nb.info/gnd/4044779-0 |
| title | Lie's structural approach to PDE systems / |
| title_auth | Lie's structural approach to PDE systems / |
| title_exact_search | Lie's structural approach to PDE systems / |
| title_full | Lie's structural approach to PDE systems / Olle Stormark. |
| title_fullStr | Lie's structural approach to PDE systems / Olle Stormark. |
| title_full_unstemmed | Lie's structural approach to PDE systems / Olle Stormark. |
| title_short | Lie's structural approach to PDE systems / |
| title_sort | lie s structural approach to pde systems |
| topic | Differential equations, Partial Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037915 Équations aux dérivées partielles Solutions numériques. MATHEMATICS Differential Equations Partial. bisacsh Differential equations, Partial Numerical solutions fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Partielle Differentialgleichung gnd http://d-nb.info/gnd/4044779-0 Partiële differentiaalvergelijkingen. gtt Lie-groepen. gtt Équations aux dérivées partielles Analyse numérique. ram |
| topic_facet | Differential equations, Partial Numerical solutions. Équations aux dérivées partielles Solutions numériques. MATHEMATICS Differential Equations Partial. Differential equations, Partial Numerical solutions Lie-Algebra Partielle Differentialgleichung Partiële differentiaalvergelijkingen. Lie-groepen. Équations aux dérivées partielles Analyse numérique. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569323 |
| work_keys_str_mv | AT stormarkolle liesstructuralapproachtopdesystems |