Exponential Stability and Numerical Results of a Coupled System of Wave Equations with Indirect Control

Authors

J. A. J. Avila, Department of Mathematics, Federal University of Sa ̃o Joa ̃o del-Rei, 36307-904, Sa ̃o Joa ̃o del Rei, MG, BrazilFollow
R. F. C. Lobato, Faculty of Exact Sciences and Technology, Federal University of Para ́, 68440-000, Abaetetuba, PA, BrazilFollow
J. A. D. Chuquipoma, Department of Mathematics, Federal University of Sa ̃o Joa ̃o del-Rei, 36307-904, Sa ̃o Joa ̃o del Rei, MG, BrazilFollow
M. J. Dos Santos, Faculty of Exact Sciences and Technology, Federal University of Para ́, 68440-000, Abaetetuba, PA, BrazilFollow

Author Country (or Countries)

Brazil

Abstract

The present paper addresses a coupled system of waves with indirect control. First, using Semigroup Theory we prove the existence of solution applying the Lumer-Phillips theorem. We show the exponential decay of the solution using Nakao’s method. Computational experiments are conducted in the one-dimensional case in order to show that the dissipative energy properties are present. To obtain the time behavior of the energy of system, we resolve two numerical tests. Finally, in both tests, we conclude that the system, for one-dimensional case, is dissipative with exponential stability.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140306

Recommended Citation

A. J. Avila, J.; F. C. Lobato, R.; A. D. Chuquipoma, J.; and J. Dos Santos, M. (2020) "Exponential Stability and Numerical Results of a Coupled System of Wave Equations with Indirect Control," Applied Mathematics & Information Sciences: Vol. 14: Iss. 3, Article 6.
DOI: http://dx.doi.org/10.18576/amis/140306
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss3/6