In this paper, the author consider conditions of that initial boundary value to study the dynamic behavior for Generalized Burgers equation, and give these system for that new conditions of blow-up, and Extinction Phenomenon of these equation with in rich using engineering. Such as, these theories and method can be used in other similar systems, they have a wide range of applications. Finale, some numerical simulations are carried out to support these new results. The authors extend dynamic behavior and the critical value to continuum more previous work [3, 9, 13] for in-depth achieve for apply value.