Formal Algorithmic Elimination for PDEs

  • Daniel┬áRobertz
Part of the Lecture Notes in Mathematics book series (LNM, volume 2121)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Daniel Robertz
    Pages 1-4
  3. Daniel Robertz
    Pages 5-117
  4. Back Matter
    Pages 233-285

About this book

Introduction

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.

Keywords

Differential algebra Differential elimination Exact solutions to partial differential equations Janet bases Thomas decomposition

Authors and affiliations

  • Daniel┬áRobertz
    • 1
  1. 1.Plymouth University School of Comp & MathPlymouthUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11445-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-11444-6
  • Online ISBN 978-3-319-11445-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book