Classical and generalized solutions of time-dependent linear differential-algebraic equations

Abstract

A coordinate-free reduction procedure is developed for linear time-dependent differential-algebraic equations that transforms their solutions into solutions of smaller systems of ordinary differential equations. The procedure applies to classical as well as distribution solutions. In the case of analytic coefficients the hypotheses required for the reduction not only are necessary for the validity of the existence and uniqueness results, but even allow for the presence of singularities. Straightforward extensions including undetermined systems and systems with nonanalytic coefficients are also discussed.