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001 978-3-319-11445-3
003 DE-He213
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007 cr nn 008mamaa
008 141013s2014 gw | s |||| 0|eng d
020 _a9783319114453
_9978-3-319-11445-3
024 7 _a10.1007/978-3-319-11445-3
_2doi
050 4 _aQA247-QA247.45
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512.3
_223
100 1 _aRobertz, Daniel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFormal Algorithmic Elimination for PDEs
_h[electronic resource] /
_cby Daniel Robertz.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aVIII, 283 p. 6 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2121
505 0 _aIntroduction -- 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.
520 _aInvestigating 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.
650 0 _aField theory (Physics).
650 0 _aAlgebra.
650 0 _aDifferential equations, partial.
650 1 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
650 2 4 _aCommutative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11043
650 2 4 _aAssociative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11027
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319114460
776 0 8 _iPrinted edition:
_z9783319114446
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2121
856 4 0 _uhttps://doi.org/10.1007/978-3-319-11445-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9436
_d9436