1.

Record Nr.

UNISA996213651403316

Autore

Robertz Daniel

Titolo

Formal Algorithmic Elimination for PDEs [[electronic resource] /] / by Daniel Robertz

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014

ISBN

3-319-11445-X

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (VIII, 283 p. 6 illus., 3 illus. in color.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2121

Disciplina

512.94

Soggetti

Algebra

Field theory (Physics)

Commutative algebra

Commutative rings

Associative rings

Rings (Algebra)

Partial differential equations

Field Theory and Polynomials

Commutative Rings and Algebras

Associative Rings and Algebras

Partial Differential Equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Includes Index.

Nota di contenuto

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.

Sommario/riassunto

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.