TY - JOUR
T1 - Long-time Asymptotic for the Damped Boussinesq Equation in a Circle
JO - Journal of Partial Differential Equations
VL - 2
SP - 97
EP - 113
PY - 2005
DA - 2005/05
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5347.html
KW - Damped Boussinesq equation
KW - initial-boundary value problem
KW - long-time asymptotics
AB - <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>