Gunther Reißig.

On properties of solutions of differential-algebraic equations.

Preprint ET-IEE-2-1994, Techn. Univ. Dresden, Fak. ET, 24 Jan. 1994

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**Abstract:**

Impasse point is a phenomenon of Differential-Algebraic
Equations (DAEs), which also occurs in the analysis of
electrical networks. It is usually characterized by the
condition that solutions of the DAE in question cannot be
continued beyond this point. However, it turns out that
several classes of impasse points, each of which represents
different behavior of the DAE, do exist. In this paper,
relations between these classes and between impasse points
and pseudo limit points are examined for the first time.
Sufficient conditions for a point to be an impasse are given
and the existence of maximal continuated solutions is proved.
Considerations include non-autonomous and degenerate DAEs as
well as non-differentiable solutions. Further, not any set
occuring in the analysis of DAEs is assumed to be a
manifold.

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