LEADER 02442cam a2200361 i 4500 001 991002946249707536 008 160715s2014 sz a ob 001 0 eng d 020 $a9783319114446 035 $ab14258407-39ule_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 /$cDaniel Robertz 260 $aCham [Switzerland] :$bSpringer,$cc2014 300 $avi, 283 p. ;$bill. ;$c24 cm 440 0$aLecture notes in mathematics,$x0075-8434 ;$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 0 $aPrinted edition:$z9783319114446 907 $a.b14258407$b17-11-16$c15-07-16 912 $a991002946249707536 945 $aLE013 12H ROB11 (2014)$g1$i2013000293608$lle013$op$pE46.79$q-$rl$s- $t0$u1$v0$w1$x0$y.i15787515$z17-11-16 996 $aFormal algorithmic elimination for PDEs$91388028 997 $aUNISALENTO 998 $ale013$b15-07-16$cm$da $e-$feng$gsz $h0$i0 LEADER 01612oam 2200529zu 450 001 9910678020403321 005 20251116151856.0 010 $a3-527-61388-9 010 $a3-527-61389-7 035 $a(CKB)1000000000376218 035 $a(SSID)ssj0000353842 035 $a(PQKBManifestationID)11301777 035 $a(PQKBTitleCode)TC0000353842 035 $a(PQKBWorkID)10288275 035 $a(PQKB)10770642 035 $a(OCoLC)184983886 035 $a(OCoLC)430953940 035 $a(OCoLC)813108108 035 $a(EXLCZ)991000000000376218 100 $a20160829d1999 uy 101 0 $aeng 135 $aurnn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAmmonia : principles and industrial practice 210 31$a[Place of publication not identified]$cWiley VCH$d1999 215 $a1 online resource (ix, 301 pages) 225 1 $aPublic health statement 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-527-29593-3 606 $aAmmonia 606 $aChemical Engineering$2HILCC 606 $aChemical & Materials Engineering$2HILCC 606 $aEngineering & Applied Sciences$2HILCC 615 0$aAmmonia. 615 7$aChemical Engineering 615 7$aChemical & Materials Engineering 615 7$aEngineering & Applied Sciences 676 $a661/.34 700 $aAppl$b Max$0754103 712 02$aUnited States.$bAgency for Toxic Substances and Disease Registry.$bDivision of Toxicology. 801 0$bPQKB 906 $aBOOK 912 $a9910678020403321 996 $aAmmonia$91517280 997 $aUNINA