03903nam 22007575 450 99621365140331620200630210719.03-319-11445-X10.1007/978-3-319-11445-3(CKB)3710000000269657(SSID)ssj0001372630(PQKBManifestationID)11761806(PQKBTitleCode)TC0001372630(PQKBWorkID)11305621(PQKB)11342794(DE-He213)978-3-319-11445-3(MiAaPQ)EBC5596471(PPN)182097463(EXLCZ)99371000000026965720141013d2014 u| 0engurnn|008mamaatxtccrFormal Algorithmic Elimination for PDEs[electronic resource] /by Daniel Robertz1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (VIII, 283 p. 6 illus., 3 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2121Includes Index.3-319-11444-1 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.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.Lecture Notes in Mathematics,0075-8434 ;2121AlgebraField theory (Physics)Commutative algebraCommutative ringsAssociative ringsRings (Algebra)Partial differential equationsField Theory and Polynomialshttps://scigraph.springernature.com/ontologies/product-market-codes/M11051Commutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Algebra.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.512.94Robertz Danielauthttp://id.loc.gov/vocabulary/relators/aut716368MiAaPQMiAaPQMiAaPQBOOK996213651403316Formal algorithmic elimination for PDEs1388028UNISA