WIAS Preprint No. 2870, (2021)

Existence, uniqueness, and stabilization results for parabolic variational inequalities


  • Kröner, Axel
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296
  • Rodrigues, Sérgio

2020 Mathematics Subject Classification

  • 35K85 93D15


  • Exponential stabilization, Parabolic variational inequalities, Oblique projection feedback, Moreau-Yosida approximation




In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau--Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions.

Appeared in

  • ESAIM: Control, Optimisation and Calculus of Variations, 29 (2023), pp. 37/1--37/38.

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