Titlebook: Infinite-Dimensional Dynamical Systems in Mechanics and Physics; Roger Temam Book 19881st edition Springer-Verlag New York Inc. 1988 calcu

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The Cone and Squeezing Properties. Inertial Manifolds,ns and generalizations C. Foias, G. Sell, and R. Temam [1], [2], C. Foias, B. Nicolaenko, G. Sell, and R. Temam [1], [2]. The reader is referred to Remark 4.3 for some bibliographical references on this rapidly expanding subject.

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,Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equse, we present briefly the physical model and the governing equations; then we present the mathematical setting of the equations which leads to the introduction of the corresponding semigroup {S(t)}.≥0.

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Springer-Verlag New York Inc. 1988

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,General Introduction. The User’s Guide,In this General Introduction we intend to focus on the general motivations and general ideas underlying this work, separating them from the mathematical technicalities, and thus developing further the presentation in the Preface.

Obligatory

Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some PhysicaThis chapter is aimed at applying the general results of Chapter V to the attractors of all the physical equations that we have considered in Chapters III and IV. It appears as one of the culminating points of the theory of attractors for dissipative partial differential equations presented in this book.

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Non-Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions,Three different topics are addressed in this chapter:.The first one is that of non-well-posed problems.