On a Time and State Dependent Maximal Monotone Operator Coupled with a Sweeping Process with Perturbations

Abstract

In this paper, we state, in separable Hilbert spaces, the existence of absolutely continuous solutions for a couple of evolution problems governed by time and state dependent maximal monotone operator and closed convex sweeping process, with perturbations.

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Acknowledgments

The authors thank the referees and the associated editor for the constructive remarks and suggestions that helped to improve the first version of the manuscript.

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Correspondence to Dalila Azzam-Laouir.

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Benguessoum, M., Azzam-Laouir, D. & Castaing, C. On a Time and State Dependent Maximal Monotone Operator Coupled with a Sweeping Process with Perturbations. Set-Valued Var. Anal 29, 191–219 (2021). https://doi.org/10.1007/s11228-020-00544-2

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Keywords

  • Absolutely continuous
  • Maximal monotone operator
  • Pseudo-distance
  • Sweeping process

Mathematics Subject Classification 2010

  • 34A60
  • 28C20
  • 28A25