Infinite-Dimensional Dynamical Systems An Introduction to Dissipa… 9780521632041
Infinite-Dimensional Dynamical SystemsAn Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors\nAuthor(s): James C. Robinson\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521632041, 978-0521632041\nSynopsis\nThis 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 conc.
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