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

Open Access

Original research article

Author(s):

Medjahed Djilali^a, Ali Hakem^b

^a Department of Mathematics, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria
^b Laboratory ACEDP, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria

Advances in the Theory of Nonlinear Analysis and its Applications 2(4), 217-223.

Received: April 25, 2018

Accepted: December 11, 2018

Published: December 12, 2018

Abstract

The purpose of this work is to study the exponential decay of energy for the one-dimensional transmission wave equation with a boundary velocity feedback.
Using the perturbed energy method developed by several authors in various contexts, and under certain conditions, we prove that the feedback controller exponentially stabilizes the equilibrium of the system to zero, i.e., the feedback leads to faster energy decay.

Keywords: Boundary feedback, decay rate of energy, exponential stabilization, perturbed energy, transmission wave equation.

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APA Style

Djilali, M., & Hakem, A. (2018). Exponential stabilization of solutions for the 1-D transmission wave equation with boundary feedback. Advances in the Theory of Nonlinear Analysis and its Application, 2(4), 217-223.