EVOLUTION PROBLEMS IN THE MECHANICS OF VISCOPLASTIC MEDIA

We obtain conditions that a Cauchy problem for a differential inclusion arising in the mechanics of visco-plastic media be well posed. We establish the complete continuity of shift; operators along the trajectory of the inclusion. We obtain variants of the Kneser-Fukuhara theorem on the structure of an integral vortex and an analogue of the first Bugolyubov theorem on the averaging of differential equations.