Abstract
This chapter discusses the concept of global attractors in partial differential equations (PDE). A global attractor is the minimal set among all compact sets that attract all bounded sets. A global attractor is the maximal set among all bounded strictly invariant sets. Sometimes, global attractors are called maximal attractors or minimal attractors. A global attractor always contains all equilibria and unstable manifolds through them. This fact is used to obtain lower estimates of dimension of global attractors. Since the definition is global, to apply this definition to semigroups generated by PDE usually one has to modify the nonlinearity outside an absorbing ball to make it globally Lipschitz. To prove the existence of an inertial manifold instead of using smallness of the nonlinearity that is used in local theorems one may use other parameters. A natural large parameter is the dimension of the manifold.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
