Geodesic
Energy decay for degenerate Kirchhoff equations with weakly nonlinear dissipation
Electronic journal of differential equations, Tome 2013 (2013)
In this article we consider a degenerate Kirchhoff equation wave equation with a weak frictional damping,

$ (|u_t|^{l-2}u_t)_t-\Big( \int_{\Omega }|\nabla _x u|^{2}\,dx\Big)^{\gamma } \Delta _xu+\alpha (t)g(u_t)=0. $

We prove general stability estimates using some properties of convex functions, without imposing any growth condition at the frictional damping term.
Classification : 35B37, 35L55, 74D05, 93D15, 93D20
Keywords: decay of solutions, nonlinear, degenerate, Kirchhoff equation 
@article{EJDE_2013__2013__a157,
     author = {Abdelli,  Mama and Messaoudi,  Salim A.},
     title = {Energy decay for degenerate {Kirchhoff} equations with weakly nonlinear dissipation},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1308.35034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a157/}
}
TY  - JOUR
AU  - Abdelli,  Mama
AU  - Messaoudi,  Salim A.
TI  - Energy decay for degenerate Kirchhoff equations with weakly nonlinear dissipation
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a157/
LA  - en
ID  - EJDE_2013__2013__a157
ER  - 
%0 Journal Article
%A Abdelli,  Mama
%A Messaoudi,  Salim A.
%T Energy decay for degenerate Kirchhoff equations with weakly nonlinear dissipation
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a157/
%G en
%F EJDE_2013__2013__a157
Abdelli,  Mama; Messaoudi,  Salim A. Energy decay for degenerate Kirchhoff equations with weakly nonlinear dissipation. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a157/