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Mathematical Modelling

On global in time solutions for differential-algebraic equations

Yu. E. Gliklikh

Voronezh State University, Voronezh, Russian Federation

Abstract: We investigate differential-algebraic equations arising in mathematical models that describe some radio-technical devises. A class of differential-algebraic equations is described, for which necessary and sufficient conditions for global in time existence of solutions are proved. As well as in many papers where sufficient conditions for such equations are obtained, we reduce them to ordinary differential equations and then apply the necessary and sufficient conditions for the latter. We deal with the systems whose matrix pencil is regular and (for simplicity) the characteristic polynomial satisfies the rank-degree condition. We also require some additional conditions that allow us to reduce the differential-algebraic system to ordinary differential one.

Keywords: differential-algebraic equation; global existence of solution; proper function; complete Riemannian metric.

MSC: 34A09, 34A12

Received: 23.04.2014

Language: English

DOI: 10.14529/mmp140303