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  3. Lie's Structural Approach to PDE Systems
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    • Publisher:
      Cambridge University Press
      Publication date:
      April 2013
      June 2000
      ISBN:
      9780511569456
      9780521780889
      9781107403321
      DOI:
      https://doi.org/10.1017/CBO9780511569456
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.08kg, 590 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.82kg, 590 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (80)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (80)
    Information

    Book description

    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.

    Reviews

    Review of the hardback:‘… a worthwhile and successful attempt to introduce the ideas of Sophus Lie.’

    H. Boseck - Zentralblatt für Mathematik

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