Exponential stabilization of solutions for the 1-d transmission wave equation with boundary feedback

Year 2018, Volume: 2 Issue: 4, 217 - 223, 24.12.2018

Medjahed Djilali , Ali Hakem

https://doi.org/10.31197/atnaa.418379

Abstract

The purpose of this work is to study the exponential decay of the energy for

the one-dimensional transmission wave equation with a boundary velocity feedback.

Thanks to the perturbed energy method developed by some authors in several contexts, and

under certain conditions, we prove that the feedback controller exponentially stabilizes the

equilibrium to zero of the system below, i.e. the feedback leads to faster energy decay.

Keywords

Boundary feedback, decay rate of energy, exponential stabilization, perturbed energy

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