Asymptotic Solutions of Burgers Equation and Modified Burgers Equation Satisfying Flux Type Conditions

In this article, we solve exactly an initial boundary value problem (IBVP) for Burgers equation satisfying flux type conditions using Cole-Hopf transformation. Asymptotic expansions of the exact solution are obtained for different regions of the quarter plane x≥0,t≥0. We observe that travelling wave solution or stationary solution describes the large time behaviour of the solutions of the initial boundary value problem in different parameter ranges. A numerical study of the large time behaviour of solutions of Burgers equation and modified Burgers equation is also presented.