Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative   Boussinesq-Type Equation
  We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle. 
Amin Esfahani, Hamideh B. Mohammadi
math.AP