This paper addresses the analysis of 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 semigroup 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 as well as a semilinear parabolic equation with a nonlinear term involving gradients.
- Doubly nonlinear evolution equation
- Generalized Allen-Cahn equation
- Generalized semiflow
- Global attractor
- Reflexive Banach space
ASJC Scopus subject areas
- Applied Mathematics