On global in time solutions for differential-algebraic equations

Abstract

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