The Point-wise Estimates For The Solution Of Generalized BBM-Equation

In this thesis, we focus on the time-asymptotic behavior of the solu_tions to theCauchy problem for the generalized Benjamin Bona Mahony (BBM) equation,which has a nonlinear convection term in the two dimensions. The problem is as fol-lows: u_t-△u_t-η△u+(β·(?))u+divf(u)=0, x∈R~2, t>0, u(x,0)=u0(x), x∈R~2. By using the method of Green’s function combined with Fourier analysis, we obtainthe point-wise estimates of the solu_tions to the Cauchy problem for the BBM equationwhich has a nonlinear convection term in the two dimensions.