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Differential Equations, Vol. 41, No. 3, 2005, pp. 319–324. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 3, 2005, pp. 306–311. Original Russian Text Copyright c 2005 by Gichev, Angelova. ORDINARY DIFFERENTIAL EQUATIONS Quasilinear Instantaneous Processes Described by Ordinary Di erential Equations T. Gichev and R. Angelova University of Architecture, Civil Engineering, and Geodesics, So a, Bulgaria Received November 10, 2003 Commutation processes in the theory of electric circuits, an impact of two mass points, and a rapid release of mass are described by ordinary di erential equations. In all these processes, some parameters of the equations have rapidly growing absolute values. This leads in a jump- like change of the process state. The mathematical abstraction of these processes is provided by an instantaneous process in which the state is changed at a given time moment. One of the classical approaches to its construction is to use of additional postulates and relations like, for example, the commutation laws and conservation laws for charges and interlinkages in circuit theory [1, pp. 271{275] and momentum conservation law in mechanics. We naturally face the problem of developing mathematical models of instantaneous processes described by di erential equations. Models of instantaneous processes in linear
Differential Equations – Springer Journals
Published: May 26, 2005
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