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 form u t + u x x x + ( g ( u ) ) x + γ u − ν u x x = f ( t ) , where ν ⩾ 0 , γ > 0 . We prove the existence of pullback attractors A ν in H 1 ( 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.