@Article{JPDE-18-97,
author = {Yi Zhang , Qun Lin  and Shaoyong Lai },
title = {Long-time Asymptotic for the Damped Boussinesq Equation in a Circle},
journal = {Journal of Partial Differential Equations},
year = {2005},
volume = {18},
number = {2},
pages = {97--113},
abstract = {<p>The first initial-boundary value problem for the following equation u_{tt} - aΔu_{tt} - 2bΔu_t = αΔ^3u - βΔ²u + Δu + ϒΔ(u²) in a unit circle is considered. The existence of strong solution is established in the space C^0([0, ∞), H^s_r (0, 1)), s &lt; 7/2, and the solutions are constructed in the form of series in the small parameter present in the initial conditions. For 5/2 &lt; s &lt; 7/2, the uniqueness is proved. The long-time asymptotics is obtained in the explicit form.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5347.html}
}