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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Keywords

  • Evolution equations
  • moving sets
  • prox-regular sets
  • differential inequalities

Mathematics Subject Classification

34G25

References

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Suggested citation

G. Colombo, C. Kozaily. “Existence and Uniqueness of Solutions for an Integral Perturbation of Moreau's Sweeping Process.” Journal of Convex Analysis 27 (2020), No. 1, 227–236. https://doi.org/10.68381/jca27013

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press.