Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation

This article deals with a forced Burgers equation (FBE) subject to the initial function, which is continuous and summable on . Large time asymptotic behavior of solutions to the FBE is determined with precise error estimates. To achieve this, we construct solutions for the FBE with a different initial class of functions using the method of separation of variables and Cole–Hopf like transformation. These solutions are constructed in terms of Hermite polynomials with the help of similarity variables. The constructed solutions would help us to pick up an asymptotic approximation and to show that the magnitude of the difference function of the true and approximate solutions decays algebraically to 0 for large time.