Infinite-Dimensional Dynamical Systems

This Book Develops The Theory Of Global Attractors For A Class Of Parabolic Pdes Which Includes Reaction-Diffusion Equations And The Navier-Stokes Equations Two Examples That Are Treated In Detail. A Lengthy Chapter On Sobolev Spaces Provides The Framework That Allows A Rigorous Treatment Of Existence And Uniqueness Of Solutions For Both Linear Time-Independent Problems (Poisson''S Equation) And The Nonlinear Evolution Equations Which Generate The Infinite-Dimensional Dynamical Systems Of The Title. Attention Then Switches To The Global Attractor A Finite-Dimensional Subset Of The Infinite-Dimensional Phase Space Which Determines The Asymptotic Dynamics. In Particular The Concluding Chapters Investigate In What Sense The Dynamics Restricted To The Attractor Are Themselves ''Finite-Dimensional''. The Book Is Intended As A Didactic Text For First Year Graduates And Assumes Only A Basic Knowledge Of Banach And Hilbert Spaces And A Working Understanding Of The Lebesgue Integral.