Asymptotic behavior for dissipative Korteweg-de Vries equations

Stéphane Vento (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We study the large time behavior of solutions to the dissipative Korteweg-de Vrie equations $u_t+u_{xxx}+|D|^{\alpha}u+uu_x=0$ with $0<\alpha<2$. We find $v$ such that $u-v$ decays like $t^{-r(\alpha)}$ as $t\rightarrow\infty$ in various Sobolev norm.

Mots clés: KdV-like equations; dissipative dispersive equations; large time behavior

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Vento. Asymptotic behavior for dissipative Korteweg-de Vries equations. 2008. ⟨hal-00226425⟩