The decay rates of solutions of generalized Benjamin–Bona–Mahony equations in multi-dimensions

In this paper, we study the decay rates of the generalized Benjamin–Bona–Mahony equations in multi-dimensional space. By using Fourier analysis for low frequencies, and by applying the energy method for high frequencies, we obtain the L2L2 convergence rates of the solution when the initial data is in a bounded subset of the phase space H1(Rn)(n≥3). The optimum decay rate is obtained in our results since it is the same as for the heat equation.