We study the Cauchy problem for the damped Kirchhoff equation in the phase space
$\, H^{r}\times H^{r-1}$, with $r\ge{3/ 2}$. We prove global solvability
and decay of solutions when the initial data belong to an open, dense subset $B$ of
the phase space such that $B+B= H^{r} \times
H^{r-1}$.
Publié le : 2010-08-15
Classification:
Damped Kirchhoff equation,
global existence,
decay estimates,
35L70,
35B40,
35L15
@article{1284570730,
author = {Manfrin, Renato},
title = {On the global solvability of the Cauchy problem for damped
Kirchhoff equations},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 411-440},
language = {en},
url = {http://dml.mathdoc.fr/item/1284570730}
}
Manfrin, Renato. On the global solvability of the Cauchy problem for damped
Kirchhoff equations. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 411-440. http://gdmltest.u-ga.fr/item/1284570730/