Abstract and Applied Analysis
Volume 2 (1997), Issue 3-4, Pages 281-299

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

Vladimir V. Varlamov

Departamento de Matematicas y Estadistica, Universidad Nacional de Colombia, Bogota, Colombia

Received 20 November 1997

Copyright © 1997 Vladimir V. Varlamov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the damped Boussinesq equation utt2butxx=αuxxxx+uxx+β(u2)xx,x(0,π),t>0;α,b=const>0,β=constR1, 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.