Existence of a global attractor governed by differential hemivariational
inequalities with parabolic type and its applications
Abstract
In this paper, we consider an abstract system which consists of a
hemivariational inequality of parabolic type combined with a nonlinear
differential inclusion (DPHVI, for short) in the framework of Banach
spaces. The objective of this paper is fourfold. The first one is to
deal with the existence of solutions and the properties of the solution
set for parabolic hemivariational inequalities (PHVIs, for short). The
second aim is to investigate the existence of mild solutions for DPHVI
by means of a fixed point technique. The third target is to study the
existence of a global attractor for the $m$-semiflow governed by
DPHVI. Finally, the fourth goal is to illustrate an application of our
abstract results.