Asymptotic behavior for dissipative Korteweg-de Vrie equations

Details Asymptotic behavior for dissipative Korteweg-de Vrie equations Asymptotic behavior for dissipative Korteweg-de Vrie equations

2008-01-30

arxiv.org/abs/0801.4698v1

Mathematics

Analysis of PDEs

Scientific paper

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 $t\to\infty$ in various
Sobolev norm.

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