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Lecture Notes in Mathematics

Formal Algorithmic Elimination for PDEs

Authors: Robertz, Daniel

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  • Contains a detailed introduction to Janet bases and Thomas decomposition
  • Develops solutions to many elimination problems for algebraic and differential systems
  • Includes non-trivial applications to formal aspects of systems of partial differential equations
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  • ISBN 978-3-319-11445-3
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About this book

Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-319-11445-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Formal Algorithmic Elimination for PDEs
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2121
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-11445-3
DOI
10.1007/978-3-319-11445-3
Softcover ISBN
978-3-319-11444-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 283
Number of Illustrations
3 b/w illustrations, 3 illustrations in colour
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