TIME-DEPENDENT LINEAR DAES WITH DISCONTINUOUS INPUTS

Existence and uniqueness results are proved for initial-value problems associated with linear, time-varying, differential-algebraic equation s. The light-hand sides are chosen in a space of distributions allowin g for solutions exhibiting discontinuities as well as impulses. This a pproach also provides a satisfactory answer to the problem of inconsis tent initial conditions, of crucial importance for physical applicatio ns. Furthermore, our theoretical results yield an efficient numerical procedure for the calculation of the jump and impulse of a solution at a point of discontinuity. Numerical examples are given.