Optimal decay rates of solutions for a multidimensional generalized Benjamin–Bona–Mahony equation

In this paper, we study the optimal decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space (n≥3n≥3). By using Fourier transform and the energy method, we obtain the Lq(2≤q≤∞)Lq(2≤q≤∞) convergence rates of the solutions under the condition that the initial data is small. The optimal decay rates obtained in this paper are found to be the same as the decay rate for the Heat equation.