Pullback D-attractors for doubly nonlinear parabolic equations

In this paper, we study a class of doubly nonlinear parabolic equations (1.1). The nonlinearity B(u) brings great difficulties to the study of the problem. First we show that the problem has a unique solution. Then we prove that the process corresponding to the problem is norm-to-weak continuous. After that, by using Legendre transform, we obtain uniform estimates and asymptotic compactness properties that allow us to ensure the existence of pullback D-attractors for the associated process to the problem