Global existence and bounded estimate of solutions of the BBM-Burgers equation

By the construction of a Cauchy sequence in a Banach space and the global bounded estimate of solution, we obtain the global existence and the bounded estimate of solution of BBM-Burgers equation without the viscous term ({u_i} + sumlimits_{j = 1}^n {{f_j}{{left( u right)}_{{x_j}}}} - gamma {}_1Delta {u_t} + {gamma _3}{Delta ^2}u = 0) with large initial date in 4-dimension space.