Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation

Vladimir V. Varlamov
1997 Abstract and Applied Analysis  
For the damped Boussinesq equationutt−2butxx=−αuxxxx+uxx+β(u2)xx,x∈(0,π),t>0;α,b=const>0,β=const∈R1, 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
more » ... e possibility of passing to the limitb→+0in the constructed solution is investigated.
doi:10.1155/s1085337597000407 fatcat:4jlvh2duona5xbdha5u4fxvd2q