02442cam a2200361 i 4500991002946249707536160715s2014 sz a ob 001 0 eng d9783319114446b14258407-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng512.9423AMS 12H05AMS 13P10AMS 16S36AMS 35-02LC QA192.R62Robertz, Daniel716368Formal algorithmic elimination for PDEs /Daniel RobertzCham [Switzerland] :Springer,c2014vi, 283 p. ;ill. ;24 cmLecture notes in mathematics,0075-8434 ;2121Includes bibliographical references and indexIntroduction ; 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 ; IndexInvestigating 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 computedDifferential equations, PartialEliminationPrinted edition:9783319114446.b1425840717-11-1615-07-16991002946249707536LE013 12H ROB11 (2014)12013000293608le013pE46.79-l- 01010.i1578751517-11-16Formal algorithmic elimination for PDEs1388028UNISALENTOle01315-07-16ma -engsz 00