Geodesic
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping
Electronic journal of differential equations, Tome 2004 (2004)
In this paper we consider the nonlinear viscoelastic equation

$ u_{tt}-\Delta u+\int_{0}^{t}g(t-\tau)\Delta u(\tau)\,d\tau +a(x)|u_{t}|^{m}u_{t}+b|u|^{\gamma }u=0, $

in a bounded domain. Without imposing geometry restrictions on the boundary, we establish an exponential decay result, under weaker conditions than those in [3].
Classification : 35B35, 35L20, 35L70
Keywords: exponential decay, global existence, nonlinear localized damping 
@article{EJDE_2004__2004__a139,
     author = {Berrimi,  Said and Messaoudi,  Salim A.},
     title = {Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1055.35020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a139/}
}
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TI  - Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping
JO  - Electronic journal of differential equations
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%A Messaoudi,  Salim A.
%T Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping
%J Electronic journal of differential equations
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%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a139/
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%F EJDE_2004__2004__a139
Berrimi,  Said; Messaoudi,  Salim A. Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a139/