Ricardo Riaza, Roswitha März
Preprint series: Institut für Mathematik, HumboldtUniversität
zu Berlin (ISSN 08630976),
MSC 2000

34A09 Implicit equations, differentialalgebraic equations

34A30 Linear equations and systems, general
Abstract
Singular
issues arising in linear timevarying differentialalgebraic equations
are addressed in this paper. We review the use of projector methods based
upon the tractability index concept for the analysis of regular problems.
A taxonomy of singularities which describes the failing of some assumption
in the tractability index definition is then introduced. The analysis of
singular problems is focused on situations in which the degeneracy is a
minimal one, namely, equations which admit a welldefined extension of
the solution set through the singularity. In this framework, socalled
weak singularities are shown to display a nonsingular local flow despite
the singular nature of the problem, extending previous results proved for
lowindex autonomous systems. Several examples illustrate the scope of
the work.