Stability of the rarefaction wave for the generalized KdV-Burgers equation

This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation {ut+ f(u)x= μuxx+ δuxxx, μ > 0, δ ∈ R {u|t=0= u0(x) → u±, x → ±∞ Roughly speaking, under the assumption that u-< u+, the solution u(x,t) to Cauchy problem (1) satisfying supx∈R|u(x,t) - uR(x/t)| → 0 as t → ∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut+ f(u)x= 0 with Riemann initial data u(x,0) = {u-, x < 0, {u+, x> 0.