A note on the stability of the rarefaction wave of the Burgers equation

This paper is concerned with the asymptotic behavior toward the rarefaction wave u^R(x/t) of the solution of the Burgers equation with viscosity. If the initial data are suitably close to constant state u± at x=±∞, then the solution u(x, t), roughly speaking, satisfies sup_R |u -u^R| ∼t^-1/2 as t → ∞ and, except for the "neighborhoods" of the corners, x=u±t of u^R, sup |u-u^R|∼t^-1. In the proof the exact forms of u are available.