We consider the Cauchy problem for a Boussinesq-type 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.
Esfahani, A., & Mohammadi, H. B. (2017). Global Existence and Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation. Mathematical Modelling and Analysis, 22(4), 441-463. https://doi.org/10.3846/13926292.2017.1319882
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