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Infinite-Dimensional Dynamical Systems
James C. Robinson
其他書名
An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
出版Cambridge University Press, 2001-04-23
主題Mathematics / GeneralMathematics / AppliedMathematics / Differential Equations / PartialMathematics / Topology
ISBN05216320489780521632041
URLhttp://books.google.com.hk/books?id=3e4h1j9WNlwC&hl=&source=gbs_api
EBookSAMPLE
註釋This book develops the theory of global attractors for a class of parabolic PDEs that 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 systemss 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.