The global attractor of infinite—dimensional dynamical systems governed by a class of nonlinear parabolic variational inequalities and associated control problems

Abstract

In this paper, the existence and Hausdorff or Fractal dimension estiamtion of the global attractor of infinite–dimensional dynamical systems governed by a class of nonlinear parabolic variational inequakutues are atudued. Some examples are presented and some problems are proposed. Especially, the influence on the above results under controls and the relationships between global attractor and controlability or stabilizability are discussed.

Keywords:

• Multivalued nonlinear infinite–dimensional dynamical systems, Golbal attractor, Control problems

^∗This research is supported by the National Natural Science Foundation and Partially by the Foundation of Zhongshan University Advanced Research Centre

^∗This research is supported by the National Natural Science Foundation and Partially by the Foundation of Zhongshan University Advanced Research Centre

Notes

^∗This research is supported by the National Natural Science Foundation and Partially by the Foundation of Zhongshan University Advanced Research Centre