Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control

Zhiling Guo; Shugen Chai

doi:10.3934/eect.2022001

Article Contents

2022, Volume 11, Issue 5: 1813-1827. Doi: 10.3934/eect.2022001

This issue Previous Article Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions Next Article Local well-posedness of the coupled KdV-KdV systems on $ \mathbb{R} $

Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control

Zhiling Guo and
Shugen Chai^,

School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China

^*Corresponding author: Shugen Chai
^*Corresponding author: Shugen Chai

Received: June 2021

Revised: October 2021

Early access: January 2022

Published: October 2022

The first author is supported by the National Natural Science Foundation of China (No.11671240).

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Abstract

In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.

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Mathematics Subject Classification: Primary: 35L05; Secondary: 93D15.

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