Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 26, Issue.: 3
A Stabilization for a Coupled Wave System with Nonlinear and Arbitrary Damping
1Center of Exact Sciences and Technology, Federal University of Acre (UFAC) 69920-900, Rio Branco, AC, Brazil.
(1) Rodica Luca, Professor, Department of Mathematics, Gh. Asachi Technical University, Romania.
(2) Jacek Dziok, Professor, Institute of Mathematics, University of Rzeszow, Poland.
(3) Tian-Xiao He, Professor, Department of Mathematics and Computer Science, Illinois Wesleyan University, USA.
(1) Chaouchi Belkacem, Khemis Miliana University, Algeria.
(2) Anonymous, UAM Cuajimalpa, Mexico.
(3) Moses O. Oyesanya, University of Nigeria, Nigeria.
(4) Angelo Favini, Universita di Bologna, Italy.
(5) Sleyman Ogrekci, Amasya University, Turkey.
Complete Peer review History: http://www.sciencedomain.org/review-history/23216
Aims/ Objectives: In this paper, based on motivations coming from various physical applications, we consider a coupled system of the wave in a one-dimensional bounded domain with nonlinear localized damping acting in their equations. We also discuss the well-posedness and smoothness of solutions using the nonlinear semigroup theory. Then, we give the asymptotic stability and rates decay to the coupled system, based on solution of an ordinary differential equation, since the feedback functions and the localized functions satisfy some properties widely treated in obtaining uniform decay rates for solutions of semilinear wave equation. Furthermore, the result requires the obtaining of the internal observability inequality for the conservative system.
Nonlinear semigroup; holmgren's uniqueness theorem; observability.
Full Article - PDF Page 1-14
DOI : 10.9734/JAMCS/2018/38196Review History Comments