Abstract
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 (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.
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