Time-Dependent, Linear DAE's with Discontinuous Inputs

摘要

Existence and uniqueness results are proved for initial value problems associatedwith linear, time-varying, differential-algebraic equations. The right-hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses . This approach also provides a satisfactory answer to the problem of inconsistent initial conditions of crucial importance for the physical applications. 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.