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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations - Softcover

 
9781461235071: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

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Synopsis

Preface.- Acknowledgments.- 1 Presentation of the Approach and of the Main Results.- 2 The Transport of Finite-Dimensional Contact Elements.- 3 Spectral Blocking Property.- 4 Strong Squeezing Property.- 5 Cone Invariance Properties.- 6 Consequences Regarding the Global Attractor.- 7 Local Exponential Decay Toward Blocked Integral Surfaces.- 8 Exponential Decay of Volume Elements and the Dimension of the Global Attractor.- 9 Choice of the Initial Manifold.- 10 Construction of the Inertial Manifold.- 11 Lower Bound for the Exponential Rate of Convergence to the Attractor.- 12 Asymptotic Completeness: Preparation.- 13 Asymptotic Completeness: Proof of Theorem 12.1.- 14 Stability with Respect to Perturbations.- 15 Application: The Kuramoto-Sivashinsky Equation.- 16 Application: A Nonlocal Burgers Equation.- 17 Application: The Cahn-Hilliard Equation.- 18 Application: A Parabolic Equation in Two Space Variables.- 19 Application: The Chaffee-Infante Reaction-Diffusion Equation.- References.

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