Del 80 i serien Encyclopedia of Mathematics and its Applications

Lie's Structural Approach to PDE Systems

Inbunden, Engelska, 2000

AvOlle Stormark,G. -C Rota,B. Doran

2 849 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Finns i fler format (1)

Häftad

1 929 kr

Skickas inom 7-10 vardagar

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.

Produktinformation

Utgivningsdatum2000-06-15
Mått157 x 239 x 33 mm
Vikt1 080 g
FormatInbunden
SpråkEngelska
SerieEncyclopedia of Mathematics and its Applications
Antal sidor590
FörlagCambridge University Press
ISBN9780521780889

Tillhör följande kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

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 n satisfying dim n' = dim n + 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 2 or 3 first integrals; 13. Classification of hyperbolic Goursat equations; 14. Cartan's theory of Lie pseudogroups; 15. The equivalence problem; 16. Parabolic PDEs for which the Monge system admits at least two first integrals; 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.