Global existence and asymptotic behavior of the Boussinesq–Burgers system

This paper is concerned with the Boussinesq–Burgers system which models the propagation of bores by combing the dissipation, dispersion and nonlinearity. We establish the global existence and asymptotical behavior of classical solutions of the initial value boundary problem of the Boussinesq–Burgers system with the help of a Lyapunov functional and the technique of Moser iteration. Particularly we show that the solution converges to the unique constant stationary solution exponentially as time tends to infinity.