Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2121)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Formal Algorithmic Elimination for PDEs
Authors: Daniel Robertz
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-11445-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Softcover ISBN: 978-3-319-11444-6Published: 22 October 2014
eBook ISBN: 978-3-319-11445-3Published: 13 October 2014
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 283
Number of Illustrations: 3 b/w illustrations, 3 illustrations in colour
Topics: Field Theory and Polynomials, Commutative Rings and Algebras, Associative Rings and Algebras, Partial Differential Equations