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024 7 $a10.1007/978-3-319-11445-3
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100   $a20141013d2014      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aFormal Algorithmic Elimination for PDEs$b[electronic resource] /$fby Daniel Robertz
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (VIII, 283 p. 6 illus., 3 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2121
300   $aIncludes Index.
311   $a3-319-11444-1 
327   $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.
330   $aInvestigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2121
606   $aAlgebra
606   $aField theory (Physics)
606   $aCommutative algebra
606   $aCommutative rings
606   $aAssociative rings
606   $aRings (Algebra)
606   $aPartial differential equations
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aAlgebra.
615  0$aField theory (Physics).
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aPartial differential equations.
615 14$aField Theory and Polynomials.
615 24$aCommutative Rings and Algebras.
615 24$aAssociative Rings and Algebras.
615 24$aPartial Differential Equations.
676   $a512.94
700   $aRobertz$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0716368
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996213651403316
996   $aFormal algorithmic elimination for PDEs$91388028
997   $aUNISA