Some aspects on sweeping processes

Abstract : In this thesis, we were interested in the study of the existence of solutions for sweeping processes. This problem takes the form of a constrained differential inclusion involving normal cones which appears naturally in many applications such as crowd motion, elastoplasticity, mechanics, electrical circuit, etc.The aim of this work is to bring together two classes of differential inclusions. On one hand, we establish some existence results of solutions-tube for sweeping processes with uniformly prox-regular sets. On the other hand, we present existence results of monotone solutions with respect to a preorder for a mixed system of projected differential inclusions. In addition, we show that our system has a saddle-point and we provide two examples of applications.
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Wissam Latreche. Some aspects on sweeping processes. General Mathematics [math.GM]. Université de Perpignan, 2018. English. ⟨NNT : 2018PERP0011⟩. ⟨tel-02198712⟩

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