title:
Doubly nonlinear evolution equations and multivalued dynamical systems

abstract:
A couple of general theories on multivalued dynamical systems were developed
and they recently started to be applied to the study of doubly nonlinear
evolution equations. Indeed, some class of doubly nonlinear problems essentially
admits multiple solutions for one initial datum.

In this talk, we first show an example of doubly nonlinear evolution equations
of Allen-Cahn type without the uniqueness of solutions and investigate the
asymptotic behavior of its solutions. Thereafter we introduce the notion of
generalized semiflow proposed by J.M.Ball to treat multivalued dynamical systems
generated by such doubly nonlinear problems. Finally, we give an
abstract framework
on the existence of global solutions and global attractors for doubly nonlinear
evolution equations governed by subdifferential operators with non-monotone
perturbations in reflexive Banach spaces.