Geodesic
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a39,
     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},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a39/}
}
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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__a39/