CLASSICAL AND GENERALIZED SOLUTIONS OF TIME-DEPENDENT LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS

A coordinate-free reduction procedure is developed for linear time-dep endent differential-algebraic equations that transforms their solution s 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 an d uniqueness results, but even allow for the presence of singularities . Straightforward extensions including undetermined systems and system s with nonanalytic coefficients are also discussed.