Asymptotic Behavior of the Solution of the Initial Boundary Value Problem for a Boussı̇nesq Analog Equation

In this paper, the asymptotics of the solution of the initial boundary value problem for a sixth-order nonlinear partial differential equation of Boussinesq type is studied. First, the energy function is obtained. Then, apriori evaluations for this function are obtained. Then, by imposing some conditions on the function on the right-hand side of the equation and using appropriate inequalities, it is shown that the solution is asymptotically damped.