Asymptotic behavior of a solution of the Cauchy problem for the generalized damped multidimensional Boussinesq equation

This work studies the Cauchy problem for the generalized damped multidimensional Boussinesq equation. By using a multiplier method, it is proven that the global solution of the problem decays to zero exponentially as the time approaches infinity, under a very simple and mild assumption regarding the nonlinear term.