Global attractors for doubly nonlinear evolution equations with non-monotone perturbations
Analysis of PDEs
2010-08-02 v2 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.0810.0191,
title = {Global attractors for doubly nonlinear evolution equations with non-monotone perturbations},
author = {Goro Akagi},
journal= {arXiv preprint arXiv:0810.0191},
year = {2010}
}