LONG-TIME ASYMPTOTIC FOR THE DAMPED BOUSSINESQ EQUATION IN A CIRCLE

摘要

The first initial-boundary value problem for the following equation utt - a△utt - 2b△ut = α△3u - β△2u + △u + γ△(u2) in a unit circle is considered. The existence of strong solution is established in the space Co([0, ∞), HST(0, 1)), s ＜ 7/2, and the solutions are constructed in the form of series in the small parameter present in the initial conditions. For 5/2 ＜ s ＜ 7/2, the uniqueness is proved. The long-time asymptotics is obtained in the explicit form.