Geodesic
Energy decay for elastic wave equations with critical damping
Electronic Journal of Differential Equations, Tome 2014 (2014).

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

Summary: 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__a131,
     author = {Horbach, Jaqueline Luiza and Nakabayashi, Naoki},
     title = {Energy decay for elastic wave equations with critical damping},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a131/}
}
TY  - JOUR
AU  - Horbach, Jaqueline Luiza
AU  - Nakabayashi, Naoki
TI  - Energy decay for elastic wave equations with critical damping
JO  - Electronic Journal of Differential Equations
PY  - 2014
VL  - 2014
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a131/
LA  - en
ID  - EJDE_2014__2014__a131
ER  - 
%0 Journal Article
%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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a131/
%G en
%F EJDE_2014__2014__a131
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__a131/