Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions - Vladimir V. Varlamov (International Journal of Mathematics and Mathematical Sciences)
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.