In this paper, in the first part, we work on the solutions of one‐ dimensional Burgers‐Sivashinsky Equation in the bounded domain
In the second part, we consider radially symmetric solutions of this equation in two and higher dimension in a bounded domain [0, R]. In both cases, using Lyapunov function approach, we study the long time behavior of the solutions and prove that there exists a time independent bound for the
norm of the solutions. Thus in each case there exists an absorbing ball when time tends to infinity.