Asymptotic Behaviors Of Solutions For The Generalized Benjamin-Bona-Mahony-Burgers Equations With Boudary Effect.

The asymptotic behaviors of solutions are studied for the generalized BBM-Burgers equation with boundary effect in this thesis.Under the condition of small perturbation, using an L~2 -energy method proves that the global solution of corresponding general initial-boundary value problem exists and converges time-asymptotically to a stationary wave or a rarefaction wave or the superposition of these two kinds of wave for the generalized BBM-Burgers equation with one-side boundary effect.For the generalized BBM-Burgers equation with two-side boundary effect, it is proved that the solution of the general initial-boundary value problem tends to the corresponding stationary wave solution for small perturbation by the similar method.