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A geometric treatment of implicit differential-algebraic equations. (English) Zbl 0804.34004

The existence and uniqueness of implicit differential-algebraic equations are proved using a differential-geometric approach to transfer the problem into explicit ordinary differential equations and applying standard theory of ordinary differential equations. The new “geometric treatment” requires weaker rank conditions than what is usually seen. Furthermore an intrinsic index definition of DAEs is presented.

MSC:

34A09 Implicit ordinary differential equations, differential-algebraic equations
34A26 Geometric methods in ordinary differential equations
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