- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 4
- Exponential stabilization of solutions for the 1-d transmission wave equation with boundary feedback
Exponential stabilization of solutions for the 1-d transmission wave equation with boundary feedback
Authors : Medjahed Djilali, Ali Hakem
Pages : 217-223
Doi:10.31197/atnaa.418379
View : 13 | Download : 11
Publication Date : 2018-12-24
Article Type : Research
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