Journal of Convex Analysis 31 (2024), No. 4, 1273--1288
Copyright Heldermann Verlag 2024
Well-Posedness for Integro-Differential Sweeping Processes of Volterra Type
Emilio Vilches
(1) Instituto de Ciencias de la Ingenierķa, Universidad de O'Higgins, Rancagua, Chile
(2) Center for Mathematical Modeling, Universidad de Chile, Santiago, Chile
emilio.vilches@uoh.cl
We study the well-posedness of integro-differential sweeping processes of Volterra type. Using new enhanced versions of Gronwall's inequality, a reparametrization technique, and a fixed point argument for history-dependent operators, we obtain the existence of solutions and provide a fully continuous dependence result for the integro-differential sweeping process. The paper ends with an application to projected dynamical systems.
Keywords: Sweeping process, prox-regular sets, normal cone, history-dependent operator.
MSC: 34A60, 49J52, 49J53.
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