Geodesic
Energy decay for degenerate Kirchhoff equations with weakly nonlinear dissipation
Electronic Journal of Differential Equations, Tome 2013 (2013).

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

Summary: 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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a157/}
}
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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/