Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction and summary
- 2 PDE systems, pfaffian systems and vector field systems
- 3 Cartan's local existence theorem
- 4 Involutivity and the prolongation theorem
- 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics
- 6 Integration of vector field systems V satisfying dim V' = dim V + 1
- 7 Higher order contact transformations
- 8 Local Lie groups
- 9 Structural classification of 3-dimensional Lie algebras over the complex numbers
- 10 Lie equations and Lie vector field systems
- 11 Second order PDEs in one dependent and two independent variables
- 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals
- 13 Classification of hyperbolic Goursat equations
- 14 Cartan's theory of Lie pseudogroups
- 15 The equivalence problem
- 16 Parabolic PDEs and associated PDE systems
- 17 The equivalence problem for general 3-dimensional pfaffian systems in five variables
- 18 Involutive second order PDE systems in one dependent and three independent variables, solved by the method of Monge
- Bibliography
- Index
3 - Cartan's local existence theorem
Published online by Cambridge University Press: 05 April 2013
- Frontmatter
- Contents
- Preface
- 1 Introduction and summary
- 2 PDE systems, pfaffian systems and vector field systems
- 3 Cartan's local existence theorem
- 4 Involutivity and the prolongation theorem
- 5 Drach's classification, second order PDEs in one dependent variable, and Monge characteristics
- 6 Integration of vector field systems V satisfying dim V' = dim V + 1
- 7 Higher order contact transformations
- 8 Local Lie groups
- 9 Structural classification of 3-dimensional Lie algebras over the complex numbers
- 10 Lie equations and Lie vector field systems
- 11 Second order PDEs in one dependent and two independent variables
- 12 Hyperbolic PDEs with Monge systems admitting two or three first integrals
- 13 Classification of hyperbolic Goursat equations
- 14 Cartan's theory of Lie pseudogroups
- 15 The equivalence problem
- 16 Parabolic PDEs and associated PDE systems
- 17 The equivalence problem for general 3-dimensional pfaffian systems in five variables
- 18 Involutive second order PDE systems in one dependent and three independent variables, solved by the method of Monge
- Bibliography
- Index
- Type
- Chapter
- Information
- Lie's Structural Approach to PDE Systems , pp. 35 - 78Publisher: Cambridge University PressPrint publication year: 2000