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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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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