Existence, uniqueness, and stabilization results for parabolic variational inequalities
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Published:2023
Issue:
Volume:29
Page:37
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ISSN:1292-8119
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Container-title:ESAIM: Control, Optimisation and Calculus of Variations
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language:
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Short-container-title:ESAIM: COCV
Author:
Kröner Axel,Rautenberg Carlos N.,Rodrigues Sérgio S.
Abstract
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.
Funder
National Science Foundation
The Berlin Mathematics Research Center MATH+
H2020 European Research Council
Austrian Science Fund
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering