An existence result for integro-differential degenerate sweeping process with convex sets.

Year 2024, Early Access, 1 - 24

Mohamed Kecies

https://doi.org/10.15672/hujms.1449554

Abstract

In this paper, we study the well-posedness in the sense of existence and uniqueness of a solution of integrally perturbed degenerate sweeping processes, involving convex sets in Hilbert spaces. The degenerate sweeping process is perturbed by a sum of a singlevalued map satisfying a Lipschitz condition and an integral forcing term. The integral perturbation depends on two time-variables, by using a semi-discretization method. Unlike the previous works, the Cauchy’s criterion of the approximate solutions is obtained without any new Gronwall’s like inequality.

Keywords

Degenerate sweeping process, perturbation, differential inclusion, set-valued map, normal cone, maximal monotone operator, Volterra integro-differential equation

References

• [1] V. Acary, O. Bonnefon, and B. Brogliato, Nonsmooth modeling and simulation for switched circuits, Lect. Notes Electr. Eng. 69, Springer, 2011