Asymptotic behavior of solutions to dissipative Korteweg-de Vries equations

摘要

We study the large time behavior of solutions to the dissipative Korteweg-de Vries equations u_t + u_(xxx) + |D|~αu + uu_x = 0 with 0 < α < 2. We find asymptotic expansions of the solution as t → ∞ in various Sobolev norms.