Large time behavior of solutions to the generalized Burgers equations

Abstract

We study large time behavior of the solutions to the initial\nvalue problem for the generalized Burgers equation. It is\nknown that the solution tends to a self-similar solution to\nthe Burgers equation at the rate $t^{-1} \\log t$ in $L^{\\infty}$\nas $t \\to \\infty$. The aim of this paper is to show that\nthe rate is optimal under suitable assumptions and to obtain\nthe second asymptotic profile of large time behavior of the\nsolutions.