LEADER 02536cam a2200385 i 4500 001 991002946179707536 006 m o d 007 cr cnu 008 160715s2014 sz a ob 001 0 eng d 020 $a9783319114453 035 $ab14258390-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a512.94$223 084 $aAMS 12H05 084 $aAMS 13P10 084 $aAMS 16S36 084 $aAMS 35-02 084 $aLC QA192.R62 100 1 $aRobertz, Daniel$0716368 245 10$aFormal algorithmic elimination for PDEs$h[e-book] /$cDaniel Robertz 260 $aCham [Switzerland] :$bSpringer,$c2014 300 $a1 online resource (viii, 283 pages) 440 0$aLecture notes in mathematics,$x1617-9692 ;$v2121 504 $aIncludes bibliographical references and index 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 $aInvestigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed 650 0$aDifferential equations, Partial 650 0$aElimination 776 08$aPrinted edition:$z9783319114446 856 40$uhttp://link.springer.com/chapter/10.1007/978-3-319-11445-3_2$zAn electronic book accessible through the World Wide Web 907 $a.b14258390$b03-03-22$c15-07-16 912 $a991002946179707536 996 $aFormal algorithmic elimination for PDEs$91388028 997 $aUNISALENTO 998 $ale013$b15-07-16$cm$d@ $e-$feng$gsz $h0$i0