Global attractors for doubly nonlinear evolution equations with non-monotone perturbations

This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semi-group approach, since solutions of the Cauchy problem for the equation might not be unique. Moreover, the preceding abstract theory is applied to a generalized Allen-Cahn equation whose potential is divided into a convex part and a non-convex part as well as a semilinear parabolic equation with a nonlinear term involving gradients.