Geodesic
Asymptotic behavior of solutions to wave equations with a memory condition at the boundary
Electronic journal of differential equations, Tome 2001 (2001)
In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.
Classification : 39A11
Keywords: wave equations, asymptotic behavior 
@article{EJDE_2001__2001__a106,
     author = {de Lima Santos,  Mauro},
     title = {Asymptotic behavior of solutions to wave equations with a memory condition at the boundary},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0984.35025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a106/}
}
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de Lima Santos,  Mauro. Asymptotic behavior of solutions to wave equations with a memory condition at the boundary. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a106/