On the Finite Dimension of Attractors of Doubly Nonlinear Parabolic Systems with L-trajectories

where Ω is a bounded and open subset in R, with a smooth boundary ∂Ω. Problems of form (P) arise in flow in porous media, nonlinear heat equation with absorption, chemical isothermic reactions and unidirectional Non-Newtonian fluids, see [4] . Therefore, it is important to obtain information about the existence of the global attractor and its regularity. In recent years, numbers of works have contributed to the study of the single equation of the type (P). Where ai = Id, the elegant work [6, 7] plays a critical role in this area. The method is extensively used in many other works; we refer the readers to [1, 2, 3, 4, 5, 8, 9, 19] and the references therein. The basic tools that have been used are a priori estimates, degree theory and super-subsolution method. In [21], Miranville has considered the following single equation