Evolution problems in the mechanics of visco-plastic media

摘要

We obtain conditions that a Gauchy 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-Pukuhara theorem on the structure of an integral vortex and an analogue of the first Bugolyubov theorem on the averaging of differential equations.