Geodesic
Differentiability, analyticity and optimal rates of decay for damped wave equations
Electronic journal of differential equations, Tome 2012 (2012)
We give necessary and sufficient conditions on the damping term of a wave equation for the corresponding semigroup to be analytic. We characterize damped operators for which the corresponding semigroup is analytic, differentiable, or exponentially stable. Also when the damping operator is not strong enough to have the above properties, we show that the solution decays polynomially, and that the polynomial rate of decay is optimal.
Classification : 35L10, 47D06
Keywords: dissipative systems, decay rate, analytic semigroups, polynomial stability 
@article{EJDE_2012__2012__a96,
     author = {Fatori,  Luci Harue and Zegarra Garay,  Maria and Mu\~noz Rivera,  Jaime E.},
     title = {Differentiability, analyticity and optimal rates of decay for damped wave equations},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1239.35088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a96/}
}
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AU  - Muñoz Rivera,  Jaime E.
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JO  - Electronic journal of differential equations
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%A Zegarra Garay,  Maria
%A Muñoz Rivera,  Jaime E.
%T Differentiability, analyticity and optimal rates of decay for damped wave equations
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a96/
%G en
%F EJDE_2012__2012__a96
Fatori,  Luci Harue; Zegarra Garay,  Maria; Muñoz Rivera,  Jaime E. Differentiability, analyticity and optimal rates of decay for damped wave equations. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a96/