We prove existence and uniqueness of solutions for a sweeping process driven by a prox-regular moving set with an integral forcing term, where the integrand is Lipschitz with respect to the state variable. The problem is motivated by a model introduced by Brenier, Gangbo, Savaré and Westdickenberg [Sticky particle dynamics with interactions, J. Math. Pures Appl. 99 (2013) 577–617]. The proof is based on a general type of penalization.
Existence and Uniqueness of Solutions for an Integral Perturbation of Moreau's Sweeping Process
Giovanni Colombo
;KOZAILY, CHRISTELLE
2020
Abstract
We prove existence and uniqueness of solutions for a sweeping process driven by a prox-regular moving set with an integral forcing term, where the integrand is Lipschitz with respect to the state variable. The problem is motivated by a model introduced by Brenier, Gangbo, Savaré and Westdickenberg [Sticky particle dynamics with interactions, J. Math. Pures Appl. 99 (2013) 577–617]. The proof is based on a general type of penalization.
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