- 期刊
LONG-TIME ASYMPTOTICS OF SOLUTIONS OF THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR THE DAMPED BOUSSINESQ EQUATION
並列摘要
For the damped Boussinesq equation u_(tt)-2bu_(txx) = -αu_(xxxx)+ uxx + β(u^2)_(xx), x ∈ (0, π), t ＞ 0; α, b = const ＞ 0, β = const ∈ R^1, the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the solution in a certain case is examined. The possibility of passing to the limit b → +0 in the constructed solution is investigated.
並列關鍵字
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