rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Formal Algorithmic Elimination for PDEs
  name:
    name part: Robertz, Daniel.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 283 p. 6 illus., 3 illus. in color. online resource.
  abstract: 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: Introduction -- Formal Methods for PDE Systems -- Differential Elimination for Analytic Functions -- Basic Principles and Supplementary Material -- References -- List of Algorithms -- List of Examples -- Index of Notation -- Index.
  note: by Daniel Robertz.
  subject:
    topic: Mathematics
  subject:
    topic: Associative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: Algebra
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematics
  subject:
    topic: Field Theory and Polynomials
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: Associative Rings and Algebras
  subject:
    topic: Partial Differential Equations
  classification: QA161.A-161.Z
  classification: QA161.P59
  classification: 512.3
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2121
  identifier: 9783319114453
  identifier: http://dx.doi.org/10.1007/978-3-319-11445-3
  record info:
    record creation date: 141013
    record change date: 20151103124238.0
    record identifier: 978-3-319-11445-3