| 书目名称 | Formal Algorithmic Elimination for PDEs |
| 编辑 | Daniel Robertz |
| 视频video | |
| 概述 | 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 for |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .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.. |
| 出版日期 | Book 2014 |
| 关键词 | Differential algebra; Differential elimination; Exact solutions to partial differential equations; Jane |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-11445-3 |
| isbn_softcover | 978-3-319-11444-6 |
| isbn_ebook | 978-3-319-11445-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer International Publishing Switzerland 2014 |
发表于 2025-3-21 19:35:35
