Geodesic
Energy decay for elastic wave equations with critical damping
Electronic journal of differential equations, Tome 2014 (2014)
We show that the total energy decays at the rate $E_u(t) = O(t^{-2})$, as $t \to +\infty$, for solutions to the Cauchy problem of a linear system of elastic wave with a variable damping term. It should be mentioned that the the critical decay satisfies $V(x) \ge C_0(1+|x|)^{-1}$ for $C_0>2b$, where b represents the speed of propagation of the P-wave.
Classification : 35L52, 35B45, 35A25, 35B33
Keywords: elastic wave equation, critical damping, multiplier method, total energy, compactly supported initial data, optimal decay 
@article{EJDE_2014__2014__a31,
     author = {Horbach,  Jaqueline Luiza and Nakabayashi,  Naoki},
     title = {Energy decay for elastic wave equations with critical damping},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a31/}
}
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AU  - Horbach,  Jaqueline Luiza
AU  - Nakabayashi,  Naoki
TI  - Energy decay for elastic wave equations with critical damping
JO  - Electronic journal of differential equations
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VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a31/
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%A Horbach,  Jaqueline Luiza
%A Nakabayashi,  Naoki
%T Energy decay for elastic wave equations with critical damping
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a31/
%G en
%F EJDE_2014__2014__a31
Horbach,  Jaqueline Luiza; Nakabayashi,  Naoki. Energy decay for elastic wave equations with critical damping. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a31/