Lie's structural approach to PDE systems
 Responsibility
 Olle Stormark.
 Imprint
 New York : Cambridge University Press, 2000.
 Physical description
 xv, 572 p. ; 24 cm.
 Series
 Encyclopedia of mathematics and its applications v. 80.
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QA377 .S846 2000  Available 
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Description
Creators/Contributors
 Author/Creator
 Stormark, Olle, 1945
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 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 n satisfying dim n' = dim n + 1
 7. Higher order contact transformations
 8. Local Lie groups
 9. Structural classification of 3dimensional 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 3dimensional 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.
 (source: Nielsen Book Data)
 Publisher's summary

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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2000
 Series
 Encyclopedia of mathematics and its applications ; 80
 ISBN
 0521780888
 9780521780889