Daniel Robertz (RWTH Aachen University)

Title: Differential algebra for the study of singular behavior and of difference approximations of PDE systems
Abstract: Given a system of linear or nonlinear partial differential equations, various tasks like determining all power series solutions, finding all compatibility conditions, or deciding whether another given equation is a consequence of the system, require formal manipulation of the system. The Thomas decomposition method lends itself to answering such questions. It splits a differential system into finitely many so-called simple differential systems, which are formally integrable, and whose sets of analytic solutions form a partition of the original solution set. This talk gives an introduction to this method and presents a few applications: detection of singularities of differential systems, algebraic study of structural properties of nonlinear control systems, consistency check for finite difference approximations to PDE systems.