Large-Time Asymptotics for Solutions of a Generalized Burgers Equation with Variable Viscosity

In this paper, we discuss the large-time asymptotics for periodic solutions of a generalized Burgers equation with variable viscosity (GBEV). Large-time asymptotics for the solutions of the GBEV depend on the parameters present in the partial differential equation and also the period of the solution of the GBEV. Large-time asymptotic expansions of the solutions are obtained by improving the solution of the linearized GBEV for certain parametric regions via a perturbative approach. These constructed large-time asymptotics are compared with the corresponding numerical solutions and are found to be in good agreement for large time. For certain other parametric region, our numerical study suggests that the solution of the inviscid GBEV describes the large-time behavior of the periodic solutions of the GBEV.