Pullback attractors for generalized Korteweg-de Vries-Burgers equations

In this paper, we study the long-time behavior of solutions to the generalized Korteweg-de Vries-Burgers equation of the formut+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.