For the damped Boussinesq equation , 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 in the constructed solution is investigated.
"Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation." Abstr. Appl. Anal. 2 (3-4) 281 - 299, 1997. https://doi.org/10.1155/S1085337597000407