| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 37 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2023017 | |
| Published online | 09 June 2023 | |
Existence, uniqueness, and stabilization results for parabolic variational inequalities
1
Martin-Luther-Universität Halle-Wittenberg,
06099
Halle (Saale),
Germany
2
George Mason University,
Fairfax,
VA,
USA
3
Johann Radon Institute for Computational and Applied Mathematics (RICAM), OeAW,
Linz,
Austria
* Corresponding author: axel.kroener@mathematik.uni-halle.de
Received:
28
March
2021
Accepted:
15
March
2023
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.
Mathematics Subject Classification: 35K85 / 93D15
Key words: Exponential stabilization / parabolic variational inequalities / oblique projection feedback / Moreau–Yosida approximation
© The authors. Published by EDP Sciences, SMAI 2023
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