Existence and decay rates of solutions to the generalized Burgers equation

In this paper we study the generalized Burgers equation ut +(u2/2)x = f (t)uxx, where f (t)>0 for t > 0. We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L∞(R), as well it is obtained the decay rates of u in Lp norm are algebra order for p ∈ [1,∞[.  2003 Elsevier Inc. All rights reserved.