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Infinite-Dimensional Dynamical Systems Hardback: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) (in English)
James C. Robinson
(Author)
·
Cambridge University Press
· Hardcover
Infinite-Dimensional Dynamical Systems Hardback: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) (in English) - Robinson, James C.
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Synopsis "Infinite-Dimensional Dynamical Systems Hardback: An Introduction to Dissipative Parabolic Pdes and the Theory of Global Attractors (Cambridge Texts in Applied Mathematics) (in English)"
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.
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The book is written in English.
The binding of this edition is Hardcover.
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