Under- and overdetermined systems of differential equations
This survey is about the notions ``underdetermined'' and ``overdetermined'' for systems of ODEs or of PDEs. There are relatively simple approaches if one considers formal power series solutions only. A modern treatment is based on the geometric theory of jet bundles and on the algebraic dimension theory of polynomial modules. For more details see the author's monography [Involution. The formal theory of differential equations and its applications in computer algebra, Berlin: Springer (2010; Zbl 1205.35003)].
scientific article; zbMATH DE number 5808533
scientific article