International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 1, Pages 131-145
doi:10.1155/S016117129922131X
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
Departamento de Matematicas, Escuela Colombiana de Ingenieria A. A., Santafe de Bogota 14520, Colombia
Received 15 March 1997; Revised 25 April 1997
Copyright © 1999 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.
Abstract
The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its
classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.