Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions

We consider a coupled system of two nonlinear wave equations of Kirchhoff type with nonlocal boundary condition and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay at the same rate of decay of the relaxation functions, that is, the energy decays expone...

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Main Authors:	Jorge Ferreira, Ducival C. Pereira, Mauro de Lima Santos
Format:	Article
Language:	English
Published:	Texas State University 2003-08-01
Series:	Electronic Journal of Differential Equations
Subjects:	Coupled system wave equation Galerkin method asymptotic behavior boundary value problem
Online Access:	http://ejde.math.txstate.edu/Volumes/2003/85/abstr.html

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spelling	doaj-a5fe7eb59b0a45f7ad198291bdcfc92c2020-11-25T00:15:33ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-08-01200385117Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditionsJorge FerreiraDucival C. PereiraMauro de Lima SantosWe consider a coupled system of two nonlinear wave equations of Kirchhoff type with nonlocal boundary condition and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay at the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially. http://ejde.math.txstate.edu/Volumes/2003/85/abstr.htmlCoupled systemwave equationGalerkin methodasymptotic behaviorboundary value problem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jorge Ferreira Ducival C. Pereira Mauro de Lima Santos
spellingShingle	Jorge Ferreira Ducival C. Pereira Mauro de Lima Santos Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions Electronic Journal of Differential Equations Coupled system wave equation Galerkin method asymptotic behavior boundary value problem
author_facet	Jorge Ferreira Ducival C. Pereira Mauro de Lima Santos
author_sort	Jorge Ferreira
title	Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
title_short	Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
title_full	Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
title_fullStr	Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
title_full_unstemmed	Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
title_sort	stability for a coupled system of wave equations of kirchhoff type with nonlocal boundary conditions
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2003-08-01
description	We consider a coupled system of two nonlinear wave equations of Kirchhoff type with nonlocal boundary condition and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay at the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially.
topic	Coupled system wave equation Galerkin method asymptotic behavior boundary value problem
url	http://ejde.math.txstate.edu/Volumes/2003/85/abstr.html
work_keys_str_mv	AT jorgeferreira stabilityforacoupledsystemofwaveequationsofkirchhofftypewithnonlocalboundaryconditions AT ducivalcpereira stabilityforacoupledsystemofwaveequationsofkirchhofftypewithnonlocalboundaryconditions AT maurodelimasantos stabilityforacoupledsystemofwaveequationsofkirchhofftypewithnonlocalboundaryconditions
_version_	1725386316694159360

Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions

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