Global Existence of Solutions of Cauchy Problem for Generalized Bbm-Burgers Equation

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equation equation(1)ut−αΔut − βΔu + γΔ2u+∑j=1nfj(u) xj  = Δg(u)+G(u), x∈ Rn,t>0 are proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation (1) are proved when n=3,2,1. Moreover, the decay property of the solution is discussed.