Friday, October 28, 2022, 2:30pm
Differential algebra for the study of singular behavior and of difference approximations of PDE systems
Daniel Robertz (RWTH Aachen University)
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.
Different parts of the presentation are joint work with V. P. Gerdt, M. Lange-Hegermann, W. M. Seiler, M. Seiss.
Location: Raum 008/SeMath, Pontdriesch 14-16, 52062 Aachen