Geodesic
Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions
Electronic journal of differential equations, Tome 2003 (2003)
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.
Classification : 34A34, 34M30, 35B05
Keywords: coupled system, wave equation, Galerkin method, asymptotic behavior 
@article{EJDE_2003__2003__a186,
     author = {Ferreira,  Jorge and Pereira,  Ducival C. and Santos,  Mauro L.},
     title = {Stability for a coupled system of wave equations of {Kirchhoff} type with nonlocal boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1036.35141},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a186/}
}
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AU  - Santos,  Mauro L.
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JO  - Electronic journal of differential equations
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VL  - 2003
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%J Electronic journal of differential equations
%D 2003
%V 2003
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%G en
%F EJDE_2003__2003__a186
Ferreira,  Jorge; Pereira,  Ducival C.; Santos,  Mauro L. Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a186/