Exact and asymptotic solutions of Burgers’ equation on half-line

Summary In this article, we solve exactly an initial boundary value problem (IBVP) posed for Burgers’ equation on the quarter plane. Asymptotic behaviors of the solution of Burgers’ equation in different regions of the quarter plane are obtained from the exact solution. The special solutions of the Burgers’ equation, such as traveling wave solution and stationary solution, describe the large time asymptotic behaviors of the solutions of the IBVP. The important contribution here is that we give a clear picture of the competition of different terms in the exact solution and the dominance of different terms leading to different asymptotic solutions. The asymptotic expansions of the exact solution of the IBVP studied here may help us in constructing asymptotic solutions of generalized Burgers’ equations that are not explicitly solvable.