Global Existence and Temporal Decay Estimate to the Generalized BBM-Burgers Equation with Dissipative Term

Through constructing a Cauchy sequence in a Banach space, we got the local existence of the solution to the generalized Benjamin-Bona-Mahony-Burgers equation with large initial data in one space dimension. Combined with the global bounded estimate of the solution, we extended the local one to a global solution. Using energy estimate, Fourier analysis and time-frequency decomposition etc, we got L₂ decay estimate of the solution. The decay rate is the same as that of the heat equation.