Journal of Convex Analysis 27 (2020), No. 1, 227--236
Copyright Heldermann Verlag 2020
Existence and Uniqueness of Solutions for an Integral Perturbation of Moreau's Sweeping Process
Giovanni Colombo
Dip. di Matematica, Università di Padova, 35121 Padova, Italy
colombo@math.unipd.it
Christelle Kozaily
INRIA Rennes -- Bretagne Atlantique, 35042 Rennes, France
christelle.kozaily@inria.fr
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.
Keywords: Evolution equations, moving sets, prox-regular sets, differential inequalities
MSC: 34G25.
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