Pullback attractors for generalized Korteweg-de Vries-Burgers equations

Abstract

In this paper, we study the long-time behavior of solutions to the generalized Korteweg-de Vries-Burgers equation of the form. ut+uxxx+(g(u))x+γu-νuxx=f(t),where ν≥0,γ>0. We prove the existence of pullback attractors Aν in H1(R) for this equation in both cases ν = 0 and ν≥ 0. Moreover, the upper semicontinuity of the pullback attractors at ν = 0 is also investigated. © 2011 Elsevier Inc.